Preheat the oven to 450°F. Cut the eggplant in half. Place, flesh side down and skin side up, on a baking sheet that has been sprayed with cooking spray (to prevent sticking). Roast for 20 minutes, until the skin is shriveled up on top and flesh begins to char.
Meanwhile, in a bowl, mix together all of the chicken marinade ingredients. Add in the chicken, making sure to coat on all sides. Place in refrigerator for 30 minutes.
Make the quinoa according to the package instructions. Once the eggplant is done, take out and allow to cool for 5-10 minutes. Put into a food processor. Add in all ingredients, except the tahini. Pulse for 10 seconds, until it is a thick semi-smooth consistency, kind of like a chunky hummus. Add in the tahini while the processor is running. Taste and season with salt if needed. Reserve in the refrigerator until serving.
Turn down oven to 400° F.
In a large, ovenproof saucepan, sauté the onions with approximately 1 tablespoon of olive oil. Allow to soften and become transparent. Add in the chicken and then the chicken stock (the stock should cover the chicken slightly, not all the way!). Put into the oven and allow to roast for 20-25 minutes, until cooked through and a thermometer reads 165° F.
Take out the chicken, put onto a platter to rest, covered with aluminum foil.
Put the saucepan back on the oven and cook over medium-high heat, allowing the sauce-onion mixture to cook down.
Serve the chicken on top of the quinoa, top with the sauce-onion mixture and garnish with basil.
Serve the eggplant tahini dip on the side with pita.