Step 1

(Note: If using a nonstick skillet, skip this step.) To prepare a black steel skillet: Heat skillet over medium heat until it starts smoking. Spread salt in an even layer. Use several layers of paper towels to rub the salt into the skillet, releasing any impurities stuck to the bottom; be very careful, as the skillet is hot! When the bottom is smooth, turn off heat and discard salt. You have just created a clean, nonstick surface for the eggs—so you're ready to cook!

Step 2

Make clarified butter: In a small saucepan, melt 8 tablespoons (1 stick) unsalted butter over medium heat and bring to a simmer, 5–7 minutes. As white foam collects on the surface, skim off with a small ladle or spoon and discard; these are the milk solids. Reduce heat to medium-low and continue skimming until the butter is clear. Pour the clarified butter through a cheesecloth-lined strainer to catch the smaller milk solids, and set aside. (Note: Clarified butter has a higher smoke point than regular butter, allowing for cooking at higher temperatures. It can be stored in an airtight container in the refrigerator for several months.) Cut smoked salmon into ¼-inch slices. Set aside. Crack eggs into a medium bowl. Add a few pinches of salt and a few grinds of pepper. Use a fork to whisk until thoroughly combined, about 1 minute.

Step 3

Heat the black steel skillet over medium heat. Add 1 tablespoon clarified butter and swirl to coat the bottom and partway up the sides. Pour the eggs into the hot skillet. Begin quickly and gently shaking the skillet, while also stirring the eggs vigorously with a fork (or a rubber spatula, if you're using a nonstick skillet). Use small circular movements to loosen the curds and lightly scramble. While scrambling, occasionally run the fork around the edge of the skillet, moving the cooked egg back into the center, 30–45 seconds. Switch to a heatproof rubber spatula; continue shaking the skillet, loosening the cooked egg from the edges, and lightly scrambling until the eggs are half curdled, about 20 more seconds. Tap the skillet on the stovetop several times to level the eggs. Turn heat to low. Working quickly, place salmon slices in an even layer across the center of the eggs. Use a zester to add about ½ teaspoon lemon zest over the salmon, followed by chopped chives.

Step 4

Tilting the skillet slightly away from yourself, begin rolling the omelette: First, loosen the edge closest to the handle, then roll it toward the middle. Add 1 tablespoon butter to the skillet and let it melt along the exterior of the omelette.When the omelette is half-rolled, run the spatula around the far edge to release the eggs from the skillet. Then tilt the skillet more sharply and tap it firmly on the stovetop to loosen the omelette. Bang on the handle with your free hand to help the far edge begin to roll up, and use the spatula as needed to fold it toward the center of the omelette. Holding the skillet over the plate, roll the omelette and gently flip it onto the plate, seam side down.

Step 5

If necessary, use your hands or a spatula to gently perfect the shape and tuck in any loose edges. Spread remaining ½ tablespoon butter across the top of the omelette. Garnish with a spoonful of caviar on top and serve immediately.