Preheat oven to 450 degrees F. In a roasting pan toss carrots, onions, eggplant, garlic and salt and pepper with 2 tablespoons of oil. Bake 15 minutes or until golden brown.
Season lamb racks with salt and pepper. In a large skillet heat remaining oil over moderately high heat. Add racks, fat side down, and cook until golden brown on all sides. Thread branches of thyme and rosemary around bones, set racks on top of vegetables in roasting pan and roast 12 minutes. Turn and roast 10 to 12 minutes more for rare meat. Transfer racks to a cutting board, cover loosely with foil and let sit 10 minutes before carving.
Make sauce: Deglaze roasting pan with wine and stock, scraping up browned bits clinging to bottom of pan; simmer 5 minutes. Transfer deglazing liquid and vegetables to a food processor or blender and puree. Strain liquid into a saucepan and keep hot.
To serve: Stand racks on a serving platter and garnish with additional thyme and rosemary branches, if desired. Transfer sauce to a sauceboat and serve separately.