Chop the chicken into bite sized chunks. Add to a bowl with the marinade ingredients. Cover with cling film and leave in the fridge for 15 minutes or up to 24 hours.
Meanwhiel, heat your grill to the highest setting, and prepare the other ingredients. Chop the brocolli into bite siezed pieces. Crush the garlic cloves into a small bowl. Finely chop the basil. Boil your pasta in a pan of salted water according to the package intructios, then drain and set aside.
Line a grill tray with foil and place the chicken pieces on it. Grill for 7-8 minutes, or until the chicken is white all the way through. Cooking time will depend on your grill, so make sure to cut into a thick piece to check it is fully cooked.
While the chicken cooks, heat 1 tbsp olive oil in a pan on medium-high heat and add the broccoli, garlic and lemon juice. Cook until the broccoli turns bright green and goes a little crispy.
Add the chicken, crème fraîche, basil and boiled pasta and stir together until all the ingredients are heated through, around 5-10 minutes. Serve with fresh parmesan and enjoy!