Heat oven to 350℉/177℃.
Spray a 10-inch x 13.75-inch casserole with cooking spray. Set aside.
In a large bowl, whisk together eggs and broth.
Add bread, stirring to coat. Set aside.
In a large skillet, sauté bacon until crisp.
Remove bacon with a slotted spoon and drain on a lined pan, reserving grease. Set bacon aside.
To the hot grease, add onions, Brussels sprouts, mushrooms, and garlic.
Sauté until tender, 5-6 minutes.
Add cooked vegetables, bacon, and thyme to bread mixture. Mix.
Stir in parmesan, mozzarella, and gruyere.
Spoon into prepared casserole.
Bake 80-90 minutes until puffy and browned, covering with foil after 35 minutes.
Let stand 15 minutes before serving.