Preheat the oven to 350°F.
In a large bowl, whisk together the eggs, milk, salt, and pepper until well combined.
In a skillet over medium heat, melt the butter. Add the egg mixture and cook, stirring gently, until the eggs are just set but still slightly soft, about 5-7 minutes.
While the eggs are cooking, slice the croissants in half horizontally and place them on a baking sheet.
Once the eggs are cooked, remove them from the heat and stir in the cheese and cooked bacon or sausage.
Spoon the egg mixture evenly onto the bottom halves of the croissants. If desired, add a layer of fresh spinach or arugula on top.
Place the top halves of the croissants on each sandwich and bake in the preheated oven for 5-7 minutes, or until the croissants are warm and slightly crispy.
Remove from the oven, slice in half if desired, and serve immediately.