Preheat Oven to 375degF. Start water boiling for pasta.
In a sauce pan over medium-high heat, add chicken, garlic and broth. Bring to boil and cook for 15 minutes. Remove chicken to mixing bowl and shred.
Once water is boiling, add jumbo shells and cook as directed on package. Drain in colander and rinse with cool water. Then toss in oil (this helps prevent sticking).
Add pesto ingredients to food processer. Blitz until creamy.
Add ¾ of pesto to shredded chicken and toss to coat.
Place a chunk of cheese into a cooked shell and add a portion of pesto chicken. Line up in baking dish and repeat with remaining shells. Spoon remaining sauce over top of shells and then sprinkle with shredded mozzarella. Place in oven and bake for 15 minutes.
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