Lightly butter a 9 by 13-inch baking dish.
Add the croissant pieces, Boursin, mozzarella, ¼ cup of the parmesan, chopped scallions, and chopped parsley to the dish and toss to combine.
In a large bowl, whisk the eggs until whites and yolks are combined.
Add the cream, milk, mustard, salt, garlic powder, and a few grinds of black pepper to the same bowl and whisk until smooth.
Pour the egg mixture over the croissant mixture, pressing down on the croissants with a spatula to help coat in the egg mixture.
Top with remaining ¼ cup of Parmesan and cover with foil.
Refrigerate at least 6 hours, preferably overnight.
Preheat the oven to 350°F with a rack in the center position.
Transfer the covered baking dish to the oven and bake for 40 minutes.
Remove the foil and bake until puffed and golden brown, about 20 minutes.
Let stand for 10 minutes.
Garnish with chives and serve with hot sauce, if desired.
