In large skillet over medium high-heat, warm 2 tablespoons olive oil. Season leg quarters with ½ teaspoon salt and ½ teaspoon black pepper. Add leg quarters to pan, skin-side down. Brown chicken, turning once, 8 to 10 minutes per side. Remove chicken to plate and drain off all but 2 tablespoons oil.
Add eggplant to hot pan and cook, stirring, 5 minutes. Add remaining tablespoon olive oil, along with zucchini, onion and garlic. Cook 5 minutes, stirring occasionally.
Raise heat to high and add white wine to pan, stirring to scrape up any browned bits. Add all other ingredients, except parsley, and place chicken legs in mixture. Bring to boil, reduce heat to medium-low, cover and simmer for 35 to 40 minutes or until cooked through or until an instant read thermometer reads 170º.
To serve, place some of the eggplant ragout onto plates, top with a leg quarter and sprinkle with parsley.