Preheat oven to 400 F. Place brussels sprouts into a saucepan and cover with water. Bring to a boil over medium heat. Let cook until fork tender. Drain and place into a baking dish.
In a large saucepan over medium heat, melt butter. Add in garlic and cook for a minute, until fragrant. Add in flour and cook for a minute to brown. Pour in milk, add salt, pepper, and thyme. Whisk constantly until the sauce has thickened.
Pour sauce over brussels sprouts and mix together. Top with mozzarella cheese and breadcrumbs. Bake for 20-25 minutes.