1. Beat the eggs slightly — just enough to blend yolks and whites without incorporating much air. Add the milk, salt, and pepper, and stir to combine. This gentle mixing is intentional; do not whisk to a froth.
2. Place a 8- to 9-inch (20–23 cm) omelet pan or skillet over medium-high heat until hot. Add the butter and allow it to melt completely and begin to foam, 30–60 seconds, watching that it does not brown.
3. Pour the egg mixture into the pan. As it begins to set on the bottom, use a fork to prick and lift the curds, drawing set egg from the edges toward the center and allowing liquid egg to flow underneath — a technique sometimes called 'disturbing' or light scrambling. Continue until the mixture is uniformly creamy and just barely set, with no large liquid pools, 2–3 minutes.
4. Slide the pan to the hottest part of the burner (or increase heat to high) to allow the underside to brown quickly, 30–60 seconds. The omelet is ready to fold when the bottom is lightly golden and releases cleanly from the pan, and the interior is still creamy rather than dry.
5. Fold the omelet in half or in thirds and turn it out onto a warmed plate. Serve immediately.
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