How to Make It
Preheat the broiler; set a rack 5 inches from the heat. Heat 1 tablespoon of the butter in a medium nonstick ovenproof skillet. Add the shallot and thyme and cook over moderate heat, stirring, until fragrant, about 30 seconds. Add the mushrooms, season with salt and pepper and cook over moderately high heat until tender and lightly browned, about 5 minutes.
In a medium bowl, whisk the egg whites until frothy. Season with salt and pepper and beat in the remaining 1 tablespoon of melted butter. Pour the beaten whites into the skillet and cook over moderate heat until almost opaque, drawing in the edges of the omelet with a spatula as they set and tilting the pan to allow the uncooked whites to seep underneath, about 40 seconds.
Transfer the skillet to the oven and broil the omelet for about 10 seconds, or until the top is just set. Run the spatula around the edge of the omelet to release it. Fold one third of the omelet onto itself, then roll it out onto a plate in a neat shape and serve at once.