Step 1: Cook shallot in 2 Tbsp butter with 1/4 teaspoons salt and 1/8 teaspoons pepper in a 10-inch nonstick skillet over medium heat, stirring occasionally, until softened, 3 to 4 minutes.
Step 2: Stir in mushrooms and cook, stirring often, until tender, about 5 minutes.
Step 3: Stir in tarragon
Step 4: Mix
Step 5: And transfer to a bowl.
Step 6: Beat eggs with 1/4 tsp salt and 1/8 tsp pepper,to taste until well combined.
Step 7: Heat remaining Tablespoon butter in same skillet over medium-high heat until foam subsides, then add 1/2 egg mixture eggs and cook until underside is set, about 1 minute.
Step 8: With a fork, pull set eggs to center, letting uncooked eggs run underneath.
Step 9: Before eggs are completely set, add 1/2 the mushroom mixture and 1/2 the cheese to one half, on side away from handle.
Step 10: Fold other half of eggs over filling with a heatproof rubber spatula, tilting pan as you roll omelet onto a plate.
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