Whisk eggs with 3 Tbsp. water. Stir in bread crumbs; let stand 5 minutes. Add Parmesan, parsley, garlic and turkey; mix gently until well combined. Moisten hands and roll mixture into 24 1 1/2-inch balls. Transfer to a dish large enough to accommodate all meatballs. Refrigerate meatballs for 30 minutes.

Pour marinara into a wide, deep pot with a lid and warm over medium-high heat. Add meatballs (sauce will not completely cover meatballs), cover and cook 10 minutes. Uncover and turn meatballs. Cover; cook 10 minutes longer, until meatballs are no longer pink inside (cut one to test).

Preheat broiler to high. Cut rolls lengthwise and drizzle inside of each with 1 tsp. olive oil. Divide cheese among rolls and place on baking sheet. Broil until cheese is melted and bread is lightly toasted, 1 to 2 minutes.

Place three meatballs on each roll and spoon sauce over. Serve immediately.