Start to finish: 30 minutes
2 tablespoons unsalted butter, cut into 2 pieces
½ teaspoon vegetable oil
4 large eggs plus 2 large yolks, chilled
Salt and pepper
2 tablespoons shredded Gruyere cheese
4 teaspoons minced fresh chives
Adjust oven rack to middle position and heat oven to 200 degrees. Place 2 heatproof plates on rack.
Cut 1 tablespoon butter in half and set aside. Cut remaining 1 tablespoon butter into small pieces, transfer to small bowl, and place in freezer while preparing eggs and skillet, at least 10 minutes.
Meanwhile, heat oil in 8-inch nonstick skillet over low heat for 10 minutes. Crack 2 eggs into medium bowl and add 1 egg yolk. Add 1/8 teaspoon salt and pinch pepper. Break egg yolks with fork, then use fork to beat eggs at moderate pace, about 80 strokes, until yolks and whites are well combined. Stir in half of frozen butter.
When skillet is fully heated, use paper towels to wipe out oil, leaving thin film on bottom and sides of skillet. Melt ½ tablespoon reserved butter in skillet, swirling to coat. Add egg mixture and increase heat to medium-high. Use 2 chopsticks or wooden skewers to scramble eggs, using quick circular motion to move around skillet, scraping cooked egg from side of skillet as you go, until eggs are almost cooked but still slightly runny, 45 to 90 seconds. Turn off heat (remove skillet from heat if using electric burner) and smooth eggs into even layer using heat-resistant rubber spatula. Sprinkle omelet with 1 tablespoon Gruyere and 2 teaspoons chives. Cover skillet with tight-fitting lid and let sit for 1 minute for runnier omelet or 2 minutes for firmer omelet.
Heat skillet over low heat for 20 seconds, uncover, and, using rubber spatula, loosen edges of omelet from skillet. Place folded paper towel on warmed plate and slide omelet out of skillet onto paper towel so that omelet lies flat on plate and hangs about 1 inch off paper towel. Using paper towel, roll omelet into neat cylinder and set aside. Return skillet to low heat and heat for 2 minutes before repeating instructions for second omelet, starting with cracking eggs into medium bowl and adding 1 egg yolk. Serve.
Nutrition information per serving: 336 calories; 253 calories from fat; 28 g fat (13 g saturated; 0 g trans fats); 652 mg cholesterol; 769 mg sodium; 3 g carbohydrate; 0 g fiber; 0 g sugar; 17 g protein.