1 tablespoon unsalted butter
2 tablespoons finely chopped onion
Salt and pepper
1 garlic clove, minced
1 (14.5-ounce) can diced tomatoes
1 ounce Parmesan cheese, grated (1/2 cup)
2 tablespoons chopped fresh basil
1 tablespoon extra-virgin olive oil
6 (3- to 4-ounce) chicken cutlets, 1/2 inch thick, trimmed
4 ounces mozzarella cheese, shredded (1 cup)

Melt butter in medium saucepan over medium-low heat. Add onion and 1/2 teaspoon salt and cook until onion is golden brown, about 3 minutes. Add garlic and cook until fragrant, about 30 seconds.

Stir in tomatoes and their juice and mash with potato masher until coarsely ground. Increase heat to high and bring to boil, about 10 minutes. Off heat, stir in Parmesan, basil and oil. Season with salt and pepper to taste.

Pat chicken dry with paper towels and season with salt and pepper. Grill chicken over hot fire until well browned on first side, about 3 minutes.

Flip chicken over and top each cutlet with 2 tablespoons tomato sauce. Divide mozzarella among cutlets. Cover and cook until mozzarella starts to melt and chicken registers 160 degrees, about 3 minutes.

Transfer chicken to plate, tent loosely with aluminum foil, and let rest for 5 minutes. Serve, passing any remaining tomato sauce separately.