Brush butter lightly over squash halves. Cover with aluminum foil.
Bake in the preheated oven until easily pierced with a fork, about 40 minutes. Cool until easily handled, about 15 minutes.
Preheat a large skillet over medium heat. Add ground beef; cook and stir until browned, about 5 minutes. Stir in tomatoes, mushrooms, red onion, green bell pepper, garlic, oregano, basil, salt, pepper, and thyme; cook, stirring occasionally, until flavors combine, 6 to 8 minutes.
Scrape squash flesh into the skillet; mix into the beef mixture. Spoon into a large casserole dish. Fold in mozzarella cheese; top with crushed crackers.
Bake in the preheated oven until golden brown, about 40 minutes.