Preheat oven to 425 degrees . Either line a large baking sheet with parchment paper or spray with non-stick spray.
Fill a large bowl with ice and cold water, set aside.
Bring a large pot of water to a boil. Add Brussels sprouts and cook until bright green and very tender, about 10 minutes. Drain Brussels sprouts and immediately submerge them into the ice bath to cool for a couple of minutes. This will stop the cooking process. Then, drain the vegetable from the cold water. Gently pat dry to removed excess water.
On prepared baking sheet, toss Brussels sprouts with garlic, salt and pepper, and thyme. Then drizzle olive oil over Brussels sprouts.
Using the flat bottom of a small glass, press down on the Brussels sprouts to smash them into a flat patty.
Sprinkle mozzarella and Parmesan cheeses on top of each Brussels sprout.
Bake in oven until the bottoms of the sprouts are crispy and the cheese is melted and golden, about 20 minutes.