Heat oven to 350℉/177℃.
Spray a 7-inch x 10-inch casserole with cooking spray. Set aside.
Sauté onions and mushrooms in olive oil until onions are nearly translucent, 2-3 minutes.
Add garlic, and continue to cook for another 1-2 minutes. Set aside.
In a large bowl, whisk together eggs, cream, and milk.
Stir in ham, cheddar, fontina, thyme, and onion mixture.
Add bread cubes.
Season with salt and pepper.
Pour into prepared casserole and let stand for 15-20 minutes, until liquid is absorbed.
Bake for 35 minutes, or until set.