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1
Whisk eggs, milk, salt, and white pepper in a bowl until just combined; do not overbeat.
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2
Melt half the butter in a non-stick pan over medium-low heat, swirling to coat evenly.
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3
Pour egg mixture in and let sit undisturbed 20 seconds, then gently push cooked curds from edge toward center using a rubber spatula, tilting pan to allow uncooked egg to flow to edges.
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4
When eggs are still slightly underdone (soft, glossy curds, about 3–4 minutes), remove from heat and fold in remaining butter until fully incorporated.
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5
Plate immediately, garnish with chives and a pinch of sea salt; serve at once.