Melt 1 tablespoon butter in heavy small skillet over medium heat. Add mushrooms and shallots and sauté until mushrooms are tender, about 2 minutes. Season with salt and pepper. Remove from heat and mix in 1 tablespoon minced fresh parsley.
Beat 3 eggs and 2 teaspoons water in small bowl. Season with salt and pepper. Heat small omelet pan over medium-high heat. Add 1 1/2 tablespoons butter and heat until foam begins to subside. Add egg mixture. Stir eggs with fork several times, drawing back of fork across bottom of pan. Lift edges of egg and let uncooked egg flow under until top is almost set. Spoon half of cheese, then half of mushroom mixture down center of omelet. Fold omelet over filling in thirds and transfer to plate.
Make second omelet with remaining eggs, water, salt and pepper, 1 1/2 tablespoons butter, mushrooms and cheese.