Preheat the broiler. Wipe the mushroom caps with a damp paper towel. Set the mushrooms on a small baking sheet, coat lightly with nonstick vegetable-oil spray, and sprinkle with salt.
Broil, gill side down, and about 4 inches from the heat source, for 2 minutes. Turn over and broil for about 2 minutes longer or until lightly browned. Transfer to a cutting board and let cool to the touch. Cut into slices.
In a medium bowl, combine the eggs, egg whites, and half the herbs. Whisk vigorously until well blended and frothy.
Season with salt and pepper to taste.
Heat a 10-inch nonstick skillet over high heat and add the oil. Add the peppers and sauté 2 minutes or until the peppers begin to soften. Immediately pour in the eggs and scatter the mushrooms over them. Rapidly stir with a folding motion for about 2 minutes, concentrating on moving the eggs from the outside of the pan to the center until the omelet begins to set.
Reduce the heat to low and continue stirring and folding for another 2 minutes or until the omelet sets. Remove from the heat and sprinkle the goat cheese evenly over the omelet.
Roll the omelet onto a warmed platter, garnish with the remaining herbs, and serve immediately.