Preheat oven to 500 degrees F.
Separately, saute the green zucchini, yellow zucchini, eggplant, yellow bell peppers and red bell peppers, in a hot pan with olive oil for 2 minutes, mixing often. Combine the vegetables in a bowl. Heat a large saucepot. Sweat the garlic and onions in olive oil. Add tomatoes and tomato paste and cook for 3 minutes over moderate heat. Add the rest of the pre-cooked vegetables and mix. Season with salt and pepper to taste, and cook for about 10 minutes on low heat, or until just a slight crunch remains in the vegetables. Keep warm.
Heat a large saute pan. Season the lamb racks with salt and pepper. Add olive oil to the hot pan and sear the lamb racks on each side for 1 1/2 minutes. Transfer lamb to a roasting pan and place in the oven. Cooking time is 10 minutes for rare, 13 for medium rare, 16 for medium and 20 minutes for well done.
Remove lamb and let rest for at least 10 minutes, but no longer than 15 minutes. While lamb is cooking, heat stock to a boil and add 2 tablespoons butter. Whisk until butter has disappeared. Add tarragon.
Heat 6 plates. Reheat ratatouille. Add 3 tablespoons olive oil and chopped basil and parsley. In the center of the plates, put a nice sized spoon of ratatouille. Slice the lamb and arrange 3 lamb chops around the vegetables and circle with the sauce.