Pesto Spaghetti with Roasted Tomatoes and Grilled Chicken

boneless skinless chicken breasts (, grilled)

dry spaghetti

grape or cherry tomatoes (, halved)

olive oil (, divided)

packed fresh basil

garlic (, minced)

pine nuts

Salt and freshly ground black pepper

finely shredded parmesan cheese (, plus more for serving)

Red pepper flakes (, for serving (optional))