Heat a large skillet over medium-high heat. Cook and stir beef in the hot skillet until browned and crumbly, 5 to 7 minutes. Add bell peppers, onion, and garlic; saute until beginning to tenderize, about 5 minutes more.

Stir water, cornstarch, bouillon, and Worcestershire sauce together in a bowl. Add to beef mixture in skillet. Cover with a lid and reduce heat to low. Simmer until sauce thickens and veggies are tender, 7 to 10 minutes. Season with salt and pepper. Add mozzarella cheese; cover until melted, about 2 minutes. Stir to combine.

Serve beef mixture on buns, Sloppy Joe-style.