In a large skillet over medium-high heat, cook the ground breakfast sausage, breaking it apart with a spoon, until browned. Add the chopped onion and cook for another 5-7 minutes until softened. Drain any excess grease.
In a large bowl, combine the cubed bread, the cooked sausage and onion mixture, 1 1/2 cups of the Gruyère cheese, and the Parmesan cheese. Toss gently to combine. Transfer the mixture to a greased 9×13-inch baking dish and spread in an even layer.
In the same large bowl, whisk together the eggs, whole milk, heavy cream, Dijon mustard, salt, pepper, and nutmeg until smooth and fully combined.
Pour the egg custard evenly over the bread mixture in the baking dish. Gently press down on the bread to help it absorb the liquid. Sprinkle the remaining 1/2 cup of Gruyère cheese on top. Cover tightly with plastic wrap or foil and refrigerate for at least 8 hours, or overnight.
The next morning, remove the casserole from the refrigerator 30 minutes before baking. Preheat your oven to 350°F (175°C). Uncover the dish and bake for 50-60 minutes, or until the casserole is puffed, golden brown, and a knife inserted into the center comes out clean.
Let the casserole rest for 10 minutes before slicing. Garnish with fresh parsley and serve warm.