Coarse salt and ground pepper
Vegetable oil, for grates
1 1/2 pounds chicken cutlets
8 ounces medium pasta shells
1 pint cherry or grape tomatoes, halved
4 ounces fresh mozzarella, cut into 1/4-inch cubes
1/2 cup fresh parsley, chopped
1/4 cup grated Parmesan, plus more for serving
2 tablespoons butter
Bring a large pot of salted water to a boil for pasta. Meanwhile, heat grill to medium; lightly oil grates. Season chicken with salt and pepper. Grill until cooked through, 2 to 3 minutes per side. Remove from grill, and cut into thin strips, halving if long.
Cook pasta until al dente, according to package instructions. Reserve 1 cup pasta water; drain pasta, and return to pot. Add chicken, tomatoes, mozzarella, parsley, Parmesan, and butter. Toss to combine. Add reserved pasta water a little at a time to create a sauce that coats shells (you may not need all the water). Serve with more Parmesan.