1. Heat 1 tablespoon butter in 10-inch nonstick skillet over medium-high heat; when foaming subsides, add asparagus, pinch salt, and pepper to taste. Cook, stirring occasionally, for 2 minutes. Add shallot and continue cooking, stirring occasionally, until asparagus is lightly browned and tender, 2 to 4 minutes longer. Add thyme, garlic, and cayenne and cook until very fragrant, about 30 seconds. Add lemon juice and toss to coat; transfer to bowl. While asparagus cooks, beat eggs and salt and pepper to taste with fork in small bowl until combined.

2. Wipe skillet clean with paper towel. Heat remaining 1 tablespoon butter in skillet over medium-low heat; when foaming subsides, pour in eggs. Cook, without stirring, until eggs begin to set, 45 seconds to 1 minute. Using rubber spatula, lift edge of cooked egg, then tilt pan to one side so that uncooked egg runs underneath. Repeat process, working around pan edge, using spatula to gently scrape uncooked egg toward rim of skillet, until top is just slightly wet, 1 1/2 to 2 minutes. Let pan sit on heat without moving for 30 seconds. Remove pan from heat, sprinkle asparagus mixture and peppers in even layer over omelet, then sprinkle cheese evenly over asparagus. Cover and let stand until egg no longer appears wet, 4 to 5 minutes.

3. Return skillet to medium heat for 30 seconds to loosen omelet. Using rubber spatula, loosen edges of omelet from skillet. Slide omelet halfway out of pan onto serving plate. Tilt pan so top of omelet folds over itself. Cut omelet in half; using large, thin spatula, transfer to individual plates and serve immediately.

Serves 2