Preheat oven to 350 degrees F. Beat the eggs in a large bowl with the coconut milk. Set aside.
In a large skillet, add the sausage, peppers, and thyme, and cook until sausage is almost cooked through. Add the garlic and continue cooking until sausage is done. Spread this mixture in the bottom of a large baking dish.
Pour the eggs over top of the sausage mixture and bake for 20-25 minutes, until eggs are set. Allow to cool slightly before serving.