In a medium bowl, whisk eggs with milk and a pinch of salt and pepper until well combined.
In a non-stick skillet over medium heat, cook sausage patties according to package directions until heated through and browned, about 3-4 minutes per side. Transfer to a plate and keep warm.
In the same skillet, reduce heat to medium-low and add 1 tablespoon butter. Once melted, pour in egg mixture. Let set for 30 seconds, then gently stir with a spatula, pushing cooked eggs to the center. Cook until just set but still soft, about 2-3 minutes. Remove from heat.
Toast the croissant halves in a toaster or in a dry skillet over medium heat until lightly golden, about 1-2 minutes.
Assemble sandwiches: Place a slice of cheese on the bottom half of each croissant. Divide scrambled eggs evenly over cheese. Top each with 2 sausage patties (or equivalent). Place top half of croissant on top.
Serve immediately.
Tips
For extra flavor, add a drizzle of hot sauce or a slice of tomato.
To make ahead, wrap assembled sandwiches in foil and reheat in a 350°F oven for 10 minutes.