Step 1

Whisk eggs in a medium bowl until very, very well combined (there should be no strands of egg white remaining, but be careful not to incorporate too much air). To make sure eggs are really smooth, strain through a fine-mesh sieve into a small bowl.

Step 2

Heat 1 Tbsp. butter in an 8" nonstick skillet over medium heat. Once the butter just begins to foam (don't let it sizzle), add eggs and season with fleur de sel and pepper. Using a rubber spatula, stir eggs very quickly and constantly in a figure-eight pattern while simultaneously moving the skillet around in a circular motion. Scrape down the sides of the skillet as you go to avoid dry bits in your omelet.

Step 3

As soon as eggs begin to coagulate, which will take about 2 minutes, shake skillet to settle any uncooked egg. Keep stirring and moving pan in a circular motion until eggs are nearly cooked through on the bottom but still runny on top (or baveuse, as the French say), about 1 minute. Lift an edge of the omelet to check that it is holding together; the underside of the omelet should have taken on no color. Remove pan from heat and let sit 1 minute to help omelet release from skillet and maintain its smooth texture.

Step 4

Spoon dollops of cheese across the center of the omelet, working perpendicular to the skillet's handle, setting you up to hold the handle with your left hand and flip the omelet onto your plate when the time comes.

Step 5

Starting at the edge closest to the handle, immediately roll up omelet in 1½" intervals, using spatula, until halfway through. Add another 1 Tbsp. butter, then continue rolling up omelet and turn out onto a plate, seam side down.

Step 6

Rub a little butter on top of omelet (to make it shiny) and sprinkle with fleur de sel and chives.