Brush each eggplant slice with olive oil and season with salt. Overlap eggplant and tomato slices and drizzle olive oil and season with pepper and microwave for about 10 min or until fork tender, or roast in the oven for about 45 min at 350ºF/180ºC. Let rest 20 min before using. Save the rendering juice and add it to the stock. Bring stock to a boil with the thyme and parsley stems; keep hot. Meanwhile, heat up a large frying pan, add butter and olive oil and sauté diced carrots for about 5 min, stirring every so often. Add shallots and cook until fragrant; for about 5 min on medium heat. Season with salt and pepper and throw in garlic and cook for a few minutes more. Stir in quinoa and cook for 3 minutes to toast. Deglaze with wine if desired; reduce to dry. Pour hot stock and cook quinoa risotto for 10 minutes on low heat; uncovered. Turn the heat off, cover with the lid and continue to cook for 5 minutes more. Season to taste with salt and pepper to taste.
In a shallow dish, arrange quinoa along with the cooked eggplant and tomato slices (remove the tomato skin), cheese and parsley. Add topping and bake at 350ºF/180ºC for about an hour. Let rest 10 min before serving – Enjoy!