Tear or slice the smoked salmon into bite-sized ribbons. Chop the dill and slice the chives. Set the salmon aside in the refrigerator while you cook the eggs. Keeping the salmon cold until the end helps it hold its texture better when folded into the warm eggs. That cold starting temperature protects the salmon's own delicate structure from the moment it's cut right up until it finally meets the eggs, giving it a genuine head start against any softening the eggs' own residual warmth might later cause.

Toast the sourdough slices until golden and crisp at the edges but still a little tender in the center. Butter them lightly if you like. Keep warm while you finish the eggs. Stopping the toast at crisp edges but a still-tender centre, rather than toasting all the way through, keeps the bread from turning brittle enough to shatter under a fork while eating this soft, delicate egg dish.

In a large bowl, whisk together the eggs, milk or cream, salt, and black pepper until fully combined and evenly yellow. Do not over-whisk to the point of lots of foam. You want a smooth egg mixture, not a bubbly one. Stopping the whisking once the mixture looks smooth and evenly coloured, rather than continuing longer, avoids introducing excess air that could work against the dense, creamy curd texture this dish depends on.

Place a large nonstick skillet or sauté pan over low to medium-low heat. Add 45g butter and let it melt gently. Pour in the eggs and cook slowly, stirring continuously with a spatula and sweeping across the bottom and sides of the pan. Soft scrambled eggs need low heat and constant movement. High heat makes them seize, toughen, and go dry very fast. That genuinely low heat, combined with continuous, sweeping movement, is what lets the eggs set gradually into fine, creamy curds rather than seizing quickly into the tougher, drier texture higher heat would produce.

Continue stirring gently until the eggs form soft, creamy curds. Add the remaining 15g butter partway through if the eggs need a little more richness and gloss. Stop cooking when the eggs are mostly set but still visibly soft, glossy, and slightly looser than you want on the plate. The eggs should look custardy and softly mounded, not wet and runny but definitely not dry. Residual heat will continue to carry them further. Adding that reserved portion of butter partway through, rather than all of it at the start, gives you a real, deliberate opportunity to adjust the eggs' own richness and gloss right as they're finishing, based on how they're actually looking at that stage.

Remove the pan from the heat completely. Let the eggs rest for 1 to 2 minutes so the temperature drops slightly. Then fold in the smoked salmon, dill, and chives gently until just combined. Do not add the salmon while the eggs are still actively cooking over heat. The goal is to warm the salmon with the eggs' own residual heat, not to cook it. That genuine, timed cooling window is the single most important safeguard in this whole recipe — it's specifically what separates a plate of eggs with silky, gently warmed salmon from one where the fish has been inadvertently cooked, turning dry and chalky in the process.

Divide the scrambled eggs among plates. Serve with the toasted sourdough, capers, and lemon wedges. Finish with a little extra dill, chives, and black pepper on top. Serving immediately captures this dish at its intended best — the eggs' own soft, glossy texture and the salmon's silky, just-warmed quality both begin to change as the plate sits.