Preheat oven to 400°. Sprinkle chicken with salt, pepper, and paprika.

Heat oil in a 12-inch cast-iron skillet over high heat until oil just begins to smoke.

Place chicken in skillet, skin sides down; reduce heat to medium-high, and cook 15 minutes. Transfer chicken to a plate; discard drippings.

Prepare the Pesto: Process arugula, parsley, olive oil, garlic, Parmesan cheese, water, lemon juice, salt, and pepper in a food processor until smooth. Refrigerate up to 1 week.

Prepare pasta according to package directions. Toss with chicken broth and 3 Tbsp. Arugula Pesto. Add pasta mixture to skillet. Place chicken, skin sides up, on pasta.

Bake at 400° for 25 to 30 minutes. Dollop with additional Arugula Pesto.