Combine the onion, brown sugar, soy sauce, vinegar, thyme, oil, garlic, allspice and habanero pepper in the container of a food processor or blender. Process until smooth. Place the chicken into a large resealable bag, and pour in 3/4 of the sauce. Squeeze out excess air, and seal. Marinate in the refrigerator for at least one hour.

Preheat your oven's broiler.

Remove chicken from bag, and discard marinade. Broil chicken for 10 to 15 minutes, turning once to ensure even cooking. Heat remaining sauce in a small pan, and pour over chicken when serving.

Use a zoodler or a vegetable peeler with teeth to spiralize the zucchini.

Heat the oil in a pan on medium high and saute the zucchini noodles, turning them continuously, until they are soft but not soggy, about 5 minutes.

Top with parmesan cheese and serve.