Preheat your oven to 350°F (175°C).
In a large bowl, whisk together the eggs, milk, salt, and black pepper until well combined.
In a skillet, melt the butter over medium heat. Pour in the egg mixture and cook, stirring gently, until the eggs are just set but still slightly soft. Remove from heat.
Slice the croissants in half horizontally. Place the bottom halves on a baking sheet.
Layer the cooked eggs evenly over the bottom halves of the croissants.
Add a slice of bacon or a sausage patty on top of the eggs, followed by a generous sprinkle of shredded cheddar cheese.
Place the top halves of the croissants on each sandwich.
Bake in the preheated oven for 10-12 minutes, or until the cheese is melted and the croissants are warm.
Remove from the oven and garnish with fresh chives or parsley if desired. Serve immediately.