In a small bowl, combine the parsley, epazote, tomato and 1/8 cup olive oil to make a salsa. Set aside.
Heat the remaining olive oil and butter in a non stick omelet pan. Add the garlic, mushrooms and thyme and saute over medium heat until soft. If they give off juice, turn up the heat until it boils away.
Preheat the broiler. Beat the eggs, milk and salt and pepper together in a small bowl. When the mushrooms are done, pour the egg mixture into the pan. Stir until it starts to scramble; stop and push down the sides with a spatula so uncooked egg hits the pan's surface. When the eggs begin to set, remove the pan from stove and place under the broiler until eggs are no longer runny. (If your pan isn't entirely heatproof, cover the handle with aluminum foil.) Remove the pan from broiler and slide the omelet onto a plate, folding it in half as you go.
Cut in two and top each half with a spoonful of the salsa.
c.1997, M.S. Milliken & S. Feniger, all rights reserved