Preheat oven to 350°.
With food processor running, drop garlic through food chute, and process until minced. Add turkey, green onions, and artichoke hearts to the processor; process until combined.
Combine mozzarella, Parmesan, Asiago, cream cheese, mayonnaise, and pepper in a large bowl. Add turkey mixture; stir until combined. Spoon mixture into a shallow 1-quart casserole dish coated with cooking spray. Bake at 350° for 30 minutes or until bubbly and top is golden. Serve hot with Melba toast rounds.