Preheat oven to 350 degrees F. Beat the eggs with the coconut milk.
In a large oven-proof skillet, melt the butter over medium heat. Add the mushrooms and spinach and cook for 2 minutes. Add the garlic, cook for an additional minute. Season with salt and pepper.
Pour the eggs into the skillet and cook for about 5 minutes. Turn off heat and transfer pan to oven.
Bake for 10-15 minutes, until eggs are set. Cool slightly before serving.