Bring a large pot of water to a full rolling boil and add the 12g of kosher salt. Add the linguine and cook, stirring occasionally, until exactly 2 minutes shy of the package directions' al dente time. The pasta must be pulled significantly underdone because it will finish cooking in the sauce during the final tossing step — absorbing the white wine, lemon, garlic, and butter directly into the pasta's structure rather than simply being coated on the outside. Before draining, reserve 240ml of the starchy pasta cooking water in a heatproof jug and keep it warm throughout. The pasta water is the emulsifying agent that allows the butter, olive oil, and lemon juice to combine into a unified, glossy sauce rather than separating into oil floating on lemon juice. Drain the linguine without rinsing and set aside briefly.

Pat the shrimp completely dry on both sides with several layers of paper towels. The drying step is the most important preparation for achieving a proper sear — any surface moisture on the shrimp turns to steam the moment it contacts the hot oil, dropping the pan temperature and producing grey, steamed shrimp rather than the golden-crusted sear that gives this dish its flavour foundation. Season with the 3g of salt and 1g of black pepper on both sides. The 16/20 count shrimp — meaning 16 to 20 shrimp per pound — are specified because their larger size allows a 90-second sear on the first side to develop genuine golden colour before the shrimp is cooked through. Smaller shrimp cook through before any significant browning can occur. If only smaller shrimp are available, reduce the first-side sear to 60 seconds.

Heat a large skillet — stainless steel or carbon steel for maximum fond development — over medium-high heat until genuinely hot. Add 40ml of the olive oil and allow to heat until shimmering. Place the shrimp in the pan in a single layer without overlapping — work in two batches if the pan cannot accommodate all 600g with space between each piece. Crowded shrimp release moisture against their neighbours and steam rather than sear. Place each shrimp flat and leave completely undisturbed for 90 seconds. The sear requires sustained, uninterrupted contact between the shrimp's surface and the hot pan — any movement before the crust has set prevents the golden caramelisation from developing. After 90 seconds the underside should show a deep golden sear. Flip each shrimp and cook for 60 seconds on the second side — the shrimp should be just barely cooked through, still slightly translucent at the very centre, because they will finish warming through when returned to the pan at the end. Transfer to a plate immediately and allow to rest — the accumulated juices on the resting plate will be added to the sauce later and carry significant concentrated shrimp and olive oil flavour.

Without cleaning the skillet — the fond from the shrimp sear is the flavour foundation of the sauce — reduce the heat to medium and add the remaining 40ml of olive oil. Add the thinly sliced garlic and red pepper flakes simultaneously. Cook for 45–60 seconds, stirring constantly — the thin garlic slices need attentive, continuous movement at medium heat because the residual heat from the shrimp searing means the pan is still warmer than the burner setting suggests. The garlic should reach pale golden with slightly crisped edges without any slice darkening to brown — at this point its flavour is sweet, toasted, and fragrant rather than the sharp, slightly bitter character that browning produces. Pour in the 180ml of dry white wine immediately when the garlic reaches this point — the wine contact with the hot pan creates a vigorous sizzle and immediate deglazing action that lifts all the fond from the shrimp sear and dissolves it into the wine. Scrape the bottom of the pan firmly with a wooden spoon to incorporate every bit of this fond into the sauce. Allow the wine to bubble vigorously for approximately 2 minutes, reducing by approximately half — the sharp, raw alcohol edge should cook off completely, leaving the wine's fruity acidity and depth as its contribution to the sauce.

Add the 60g of butter to the reduced wine, cut into cubes for faster, more even melting. Add the zest of both lemons and the 60ml of lemon juice simultaneously. Swirl the pan continuously as the butter melts — the swirling motion emulsifies the melting butter fat into the wine and lemon juice, creating the beginning of the glossy, cohesive sauce base. The double lemon application — zest and juice together — is the technique that produces a lemon character that is both bright and acidic from the juice and deeply aromatic and complex from the zest's volatile oils. Add 180ml of the reserved pasta water and bring to a gentle simmer. Add the drained linguine and the rinsed capers to the simmering sauce. Toss vigorously with tongs for 2–3 minutes over medium heat, turning the linguine continuously through the sauce. The pasta finishes cooking during this tossing — absorbing the sauce and releasing additional starch into the liquid, progressively thickening and emulsifying the sauce further. Add reserved pasta water in 30ml increments if the pan looks dry at any point — the sauce should remain fluid and glossy throughout the tossing period.

Pour any accumulated resting juices from the shrimp plate directly into the pasta — these juices contain rendered shrimp fat, olive oil, and protein that add concentrated seafood-forward flavour to the sauce with zero additional effort. Return the seared shrimp to the pan. Add the roughly chopped parsley, torn basil leaves, and remaining 1g of black pepper. Toss gently for 30 seconds — enough to distribute the herbs and rewarm the shrimp without overcooking them. The residual heat of the pasta and sauce warms the shrimp through without additional cooking time. Remove from heat. Add the finely grated Parmigiano-Reggiano and toss quickly to incorporate — the cheese melts into the hot sauce and adds a savoury, slightly creamy depth that is not traditionally Italian for a seafood pasta but works exceptionally well with the lemon-butter character of this specific sauce. Divide immediately among four warm shallow bowls, distributing the shrimp evenly among portions. Spoon any remaining pan sauce over each bowl.