Preheat oven to 220°C and line a large baking sheet with parchment paper. Prepare an ice bath in a large bowl.
Blanch brussel sprouts: Bring a large pot of salted water to a boil. Add brussel sprouts and cook until bright green and very tender, about 10 minutes. Add brussel sprouts to ice bath to cool then drain.
On a large baking sheet, toss blanched brussel sprouts with olive oil, garlic and thyme. Using the end of a small glass or mason jar, press down on the brussels sprouts to smash them into a flat patty. Season each smashed brussel sprout with salt and pepper, then sprinkle mozzarella and Parmesan on top.
Bake until the bottoms of the sprouts are crispy and the cheese is melted and golden, about 20 minutes.