Heat oil with garlic in a shallow casserole and cook until fragrant, about 1 minute. Add the chicken pieces skin-side down. Fry over a medium-high heat until golden. Flip the pieces then sear the bottoms. Season with salt and pepper to taste. Add hot chicken broth and simmer gently for about 30 minutes turning pieces from time to time until chicken has cooked. Check the sauce every so often while it is cooking. If the sauce is getting too dry, add a splash of water/broth and gently stir.
Shred chicken pulp and put it back to the casserole together with pine nuts and raisins. Heat gently.
In the meantime, heat 7 quarts of water to boiling and add 2 tablespoons of salt. Add broccoli florets and cook 3-5 minutes. Add Tortelloni and cook according to package instructions. Drain reserving ½ cup of the pasta cooking water, add Tortelloni and broccoli to the casserole and toss to combine adding a few spoons of the cooking water if needed to loosen the sauce.
Divide Tortelloni among plates and serve.