Warm a large platter and four plates under hot tap water, then dry them, or set them in a 200°F (95°C) oven for 5 minutes.

Crack the eggs into a large bowl, add the milk, and whisk with a fork for 20 to 30 seconds until no thick, clear strands of white remain. Whisk in the kosher salt and pepper just before cooking.

Melt 2 tbsp of the cooking butter in a 10-inch nonstick skillet over medium-low heat until it foams quietly and smells sweet, about 1 minute. If it starts to brown, lift the pan off the burner for 30 seconds and lower the flame.

Pour in half of the eggs (about 1 1/4 cups) and wait 15 to 20 seconds until the edges turn opaque. Drag a silicone spatula slowly across the bottom and fold the egg over itself, 3 to 4 minutes, until small soft curds form and the surface is still wet and glossy.

Pull the pan off the heat, stir in half of the cold butter until it melts into a sheen, and slide the eggs onto the warm platter right away. Cover loosely with an upturned bowl. For young children, older adults, pregnant guests or anyone with a weakened immune system, cook the eggs until fully set and an instant-read thermometer shows 160°F (71°C).

Wipe the pan clean, stir the remaining eggs in the bowl, and repeat the cooking steps with the remaining 2 tbsp cooking butter and the rest of the cold butter.

Divide the eggs among the warm plates, scatter with the chives and a pinch of flaky sea salt, and serve immediately.