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Heat the oil (or butter) in a small skillet over medium-high heat.
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Add the mushrooms and cook until the mushrooms brown slightly. Don't crowd the mushrooms; cook in a single layer.
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Reduce the heat to medium.
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In a bowl, whisk the eggs, milk, nutmeg, Herbes de Provence, salt and pepper until frothy.
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Pour the egg mixture into the skillet.
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Cook over medium heat, loosening the eggs periodically with a spatula. Let some of the liquid spill over the side of the cooked eggs.
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When the eggs are set (no longer liquid), flip the eggs to the uncooked side to finalize the cooking.
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Spread the mushrooms over the top of the omelet and fold the cooked eggs in half to cover the mushrooms.
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Remove the omelet to a waiting plate and garnish with sliced tomatoes.