Grilled chicken, monzzarella & shells

Coarse salt and ground pepper
Vegetable oil
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
Directions
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.