Preheat the oven to 375°F (190°C).
In a large bowl, whisk together the eggs, milk, salt, and pepper until well combined.
Slice each croissant in half horizontally and place the bottom halves on a baking sheet.
In a skillet over medium heat, cook the bacon or sausage until crispy. Remove from heat and set aside.
Pour the egg mixture into the skillet and cook, stirring gently, until the eggs are just set but still slightly soft. Remove from heat.
Evenly distribute the scrambled eggs over the bottom halves of the croissants.
Top the eggs with a slice of bacon or a sausage patty, and sprinkle with shredded cheddar cheese.
Place the top halves of the croissants over the cheese.
Bake in the preheated oven for 10-12 minutes, or until the cheese is melted and the croissants are golden brown.
Remove from the oven, garnish with fresh chives or parsley if desired, and serve warm.