Preheat the oven to 400°F
Cut the eggplant in half length wise, and carefully hollow out each half leaving about a 1/4 of an inch around the sides. Roughly chop the removed eggplant.
Heat the olive oil in a large skillet over medium high heat. Add the onion sauté until tender, about 5-6 minutes.
Add the chopped eggplant, mushrooms, and garlic. Cook until the eggplant is tender, about 7-8 minutes.
Add the ground chicken, oregano, salt and pepper. Cook until the chicken is no longer pink, about 10 minutes. Stir in the roasted red peppers and basil and remove the skillet from the heat.
Place the eggplant halves in a baking dish and stuff them with the chicken mixture. Drizzle a little olive oil on top and roast for 30-35 minutes until tender.
Meanwhile, add the balsamic vinegar to a small sauce pan. Bring to a low simmer and cook until it has thickened and reduced by about half, about 10-12 minutes.
Remove the stuffed eggplants from the oven and top with the balsamic reduction and additional basil before serving.