Preheat your oven to 350°F (175°C).
In a large mixing bowl, whisk together the eggs, milk, dry mustard, salt, and black pepper until well combined.
In a greased 9x13 inch baking dish, layer the croissant pieces evenly across the bottom.
Sprinkle the cooked sausage over the croissant pieces, followed by the shredded cheddar cheese.
Pour the egg mixture evenly over the layered ingredients, ensuring everything is well soaked.
Cover the dish with plastic wrap and refrigerate for at least 2 hours, or preferably overnight to allow the croissants to absorb the egg mixture.
When ready to bake, remove the casserole from the refrigerator and let it sit at room temperature for about 15 minutes.
Bake in the preheated oven for 35-40 minutes, or until the casserole is puffed and golden brown.
Allow to cool for a few minutes before slicing and serving.