1 tablespoon chopped scallions and/or fresh herbs such as parsley, tarragon, chives, dill, or cilantro (optional)
1 tablespoon butter plus more for serving
1/4 to 1/3 cup desired filling (onion or shallot mushrooms, bell peppers, spinach, diced turkey or ham, crumbled bacon, diced potatoes, chopped asparagus, shrimp or crabmeat, cheese, seeded and diced tomatoes, prepared salsa, chopped canned artichoke hearts, diced avocado, diced smoked salmon)
Have a serving plate ready. In a medium bowl, whisk eggs until frothy. Season with salt and pepper; whisk in scallions and/or herbs, if using.
Heat butter in an 8-inch nonstick skillet over medium-high, tilting to coat pan; after foaming subsides, whisk eggs again, and add to skillet.
Cook, stirring quickly with a heatproof rubber spatula, until eggs begin to thicken, about 30 seconds. With spatula, pull edges of omelet in toward center, tilting pan so uncooked eggs flow to edges of pan and underneath omelet. Cook until just set but still loose, 15 to 30 seconds (omelet will continue to cook once removed from heat).
Sprinkle with filling. Using spatula, loosen omelet from skillet on all sides; shake pan to ensure it is completely released. Tilt pan toward serving plate; with spatula, working from side of skillet that's tilted up, fold 1/3 of omelet over the center.
Simultaneously slide and roll omelet onto plate so that it folds over on itself again and lands seam side down. Brush or dab lightly with butter; serve immediately.