Peel the potatoes and cut them into very thin matchsticks, about 2–3mm thick. A mandoline is the cleanest way to do this. Place the potatoes in ice-cold water and soak for 30 minutes to remove excess starch. Drain, rinse, and dry extremely well with towels. Do not half-dry them. Wet potatoes spit oil, fry unevenly, and turn limp instead of crisp. The cold soak draws out surface starch that would otherwise cause the thin sticks to clump together in the fryer — at this thinness, clumped potatoes fry unevenly in a way that's much harder to correct than with a standard-cut fry.

Add the ketchup, tomato paste, water, vinegar, brown sugar, mustard, smoked paprika, cumin, garlic powder, onion powder, cayenne if using, and salt to a small saucepan. Simmer over low heat for 5–7 minutes, stirring often, until glossy, slightly thicker, and smooth. Taste and adjust salt or vinegar. The sauce should be sweet, tangy, smoky, and spoonable. It should not taste like plain ketchup dumped on a burger. Simmering the ketchup base briefly with tomato paste, vinegar, and spices concentrates and rounds out its flavour in a way raw ketchup alone never would — this small amount of active cooking is what separates a genuine frita sauce from a squeeze-bottle condiment.

In a bowl, combine the ground beef, raw chorizo, grated onion, garlic, salt, smoked paprika, sweet paprika, cumin, oregano, black pepper, cayenne if using, breadcrumbs or crushed crackers, and egg. Mix only until evenly combined. Do not knead it into meat paste. Overworked patties turn dense and sausage-like in the wrong way. Mixing just until combined keeps the meat's protein structure loose enough to stay tender once cooked — overworking it develops a tighter bind that produces a noticeably denser, chewier patty, closer to a sausage puck than a proper burger.

Divide the mixture into 4 equal patties. Shape them slightly wider than the buns because they will shrink during cooking. Make a shallow indentation in the centre of each patty so it stays flatter while searing. Chill the patties for 10–15 minutes while the potatoes finish drying and the oil heats. This helps them hold together. The centre indentation counters a common tendency for burger patties to puff up and dome in the middle as they cook — starting with a slight dip there produces a flatter, more even patty by the time it's fully seared.

Heat neutral oil to 170°C. Fry the potatoes in small batches for 2–3 minutes, stirring gently so they separate, until pale golden and crisping. Transfer to a rack. Increase the oil to 185°C and fry again for 60–90 seconds until deeply golden, crisp, and dry-looking. Season immediately with fine sea salt while hot. Do not fry one giant batch. That drops the oil temperature and gives you greasy potato straw. The papitas need to be crisp enough to pile high without collapsing. This double-fry follows the same cooler-then-hotter logic used for standard fries throughout this collection, adapted to the thinner cut here — the first fry cooks the potato through and begins crisping, while the second, hotter fry drives off remaining moisture for the genuinely dry, crackling texture a proper pile of papitas needs.

Butter the cut sides of the brioche buns. Toast cut-side down in a skillet or on a griddle for 1–2 minutes until golden and lightly crisp. The bun needs structure. An untoasted bun under sauce, chorizo fat, and potatoes will get soft fast. This toast gives the soft brioche real resistance against the combined moisture of the sauce, the patty's rendered fat, and the substantial pile of potatoes stacked on top.

Heat a cast-iron skillet or griddle over medium-high heat. Add a thin film of oil only if needed. Sear the patties for 3–4 minutes on the first side until a deep paprika-red crust forms. Flip and cook another 3–4 minutes, until browned, cooked through, and juicy. Because the patties contain pork chorizo, cook them fully to 71°C internally. Do not treat them like rare beef burgers. The smoked and sweet paprika in the mix are largely responsible for that deep red crust colour developing during the sear — this isn't simply beef browning, but the paprika's own pigments concentrating and darkening against the hot surface.

During the final minute, spoon a little frita sauce over each patty and let it bubble against the hot surface. This gives the patty a glossy red finish without making it wet. Do not drown the patty. The sauce should cling and shine, not slide everywhere. Adding the sauce only in this last minute, rather than earlier in the sear, means it briefly caramelises against the hot pan rather than simply sitting wet on top — that quick contact with direct heat is what produces the glossy, clinging glaze rather than a runny coating.

Spread frita sauce on the bottom buns. Add one hot chorizo-beef patty to each bun. Spoon a little more sauce over the patty. Add optional diced white onion if using. Pile the crispy shoestring potatoes high over the patty. Close with the top bun. Piling the potatoes generously rather than sparingly is deliberate — the frita's signature silhouette depends on that abundant, visible pile of crisp potato straw rather than a token garnish.

Serve immediately while the patty is hot, the sauce is glossy, the bun is soft and toasted, and the potato sticks are still crisp. Once the hot sauce and steam hit the potato sticks, the clock is ticking. The thin, delicate shoestring potatoes lose their crackling crispness faster than a standard fry would once exposed to the patty's residual heat and steam, making prompt serving especially important for this particular burger.