Butter a 9x13-inch casserole dish. Heat oil in a large nonstick skillet over medium heat and cook the mushrooms, stirring occasionally, until lightly golden brown, 6 to 8 minutes.
While mushrooms cook, partially split croissants, making sure not to cut all the way through. Stuff with spinach and all but 1/2 cup cheese and transfer to prepared dish, cut sides facing up. Divide mushrooms among stuffed croissants.
In a bowl, beat eggs with milk and 1/2 teaspoon each salt and pepper, then pour over croissants. Sprinkle remaining 1/2 cup cheese over top. Cover with foil, then plastic wrap; refrigerate at least 15 minutes or overnight.
When ready to serve, heat oven to 375°, remove casserole from fridge, and discard plastic wrap. Bake for 20 minutes, then remove foil and bake until eggs are puffed and just set, 25 to 30 minutes more.