Place bread in a food processor; process 30 seconds or until finely ground. Place breadcrumbs in a large bowl. Add milk to breadcrumbs; toss with a fork to moisten. Add salt, pepper, and beef to breadcrumb mixture, stirring just until combined. Divide meat mixture into 16 equal portions, shaping each into a 3 1/2-inch patty. Spoon 1 tablespoon cheese in the center of each of 8 patties; top each with 1 remaining patty, pinching edges to seal.
Place patties on grill rack coated with cooking spray; grill 4 minutes on each side or until desired degree of doneness. Remove from heat; keep warm.
Lightly coat cut sides of rolls with cooking spray; place cut sides down on grill rack, and grill 30 seconds or until toasted. Serve patties on toasted rolls with desired toppings.
Wine note: Enjoy a bottle of American zinfandel with this menu. Pietra Santa Zinfandel 2003 ($16) is loaded with jammy blackberry and raspberry fruit, along with smoky oak and hints of Chinese five spice that go great with grilled flavors, yet the typically soft tannins make it versatile enough to sip throughout the meal. --Jeffery Lindenmuth