Preheat oven to 350°. Pour sauce into an 11 × 7-inch baking dish.
Whisk together flour and next 3 ingredients. Dredge chicken in flour mixture, shaking off excess.
Cook chicken in 2 Tbsp. hot oil in a large sauté pan over medium-high heat 4 minutes on each side or until browned. Transfer to baking dish. Top each tender with mozzarella cheese, and sprinkle entire dish with Parmigiano-Reggiano.
Bake at 350° for 10 to 15 minutes or until chicken is done and cheese is bubbly. Remove from oven, and sprinkle with fresh oregano. Serve over cooked spaghetti.