1. Combine first 3 ingredients in a small skillet over medium-high heat; bring to a simmer. Cook 3 minutes or until water evaporates and mushrooms are tender, stirring occasionally. Remove from heat. Stir in chopped parsley, lemon juice, and 1/8 teaspoon salt.
2. Melt 1 1/2 teaspoons butter in an 8-inch skillet over medium-high heat. Place 2 eggs in a small bowl. Add 1/8 teaspoon salt and a dash of pepper, stirring with a whisk until eggs are frothy. Pour egg mixture into pan, and stir briskly with a heatproof spatula for about 10 seconds or until egg starts to thicken. Quickly pull the egg that sets at sides of the pan to the center with the spatula, tipping the pan to pour uncooked egg to the sides. Continue this procedure for 10 to 15 seconds or until almost no runny egg remains. Remove pan from heat; arrange half of mushroom mixture (about 1 1/2 tablespoons) over omelet in pan. Run spatula around the edges and under omelet to loosen it from the pan. To fold the omelet, hold the pan handle with one hand and tip the pan away from you. Give the handle a sharp tap with your other hand so the top edge of the omelet flips over, or fold the edge over with a fork. Slide the omelet from the pan onto a plate, rolling it as it slides, so it lands folded in three with the seam underneath. Tuck in the sides of the omelet to neaten it. Repeat procedure with remaining 1 1/2 teaspoons butter, 2 eggs, 1/8 teaspoon salt, dash of pepper, and 1 1/2 tablespoons mushroom mixture.