Heat olive oil or butter in a 10-inch non-stick skillet over medium heat. Add sliced mushrooms in a single layer and cook undisturbed for 3-4 minutes, then stir occasionally until they release moisture and develop golden brown edges, about 5-7 minutes total.

Add fresh spinach directly on top of the mushrooms and stir until completely wilted, about 1-2 minutes.

While vegetables cook, crack eggs into a mixing bowl. Add milk, salt, and pepper. Whisk vigorously for 30 seconds until light and frothy.

Pour egg mixture over the cooked mushrooms and spinach. Let the eggs sit undisturbed for 10 seconds to begin setting, then gently push eggs from edges toward center using a spatula. Continue cooking over medium heat for about 2 minutes.

When eggs are mostly set but still slightly glossy on top, sprinkle cheese over them if using. Remove from heat immediately.