Preheat oven to 400°. Mince 2 garlic cloves and rub onto lamb, spreading evenly. Generously sprinkle lamb with salt and pepper. Put lamb on a V-shaped rack in a large roasting pan. Surround rack with onion, carrots, shallots, tomato, and remaining 4 garlic cloves. Drizzle olive oil over vegetables and lamb.
Roast 30 minutes. Reduce heat to 350° and cook another 30 minutes.
Reduce heat to 250°. Transfer lamb to a plate and lift rack from pan. Set the roasting pan on a burner over high heat, add wine, and boil, using a wide metal spatula to stir and scrape caramelized vegetables from bottom of pan, until wine has reduced by half. Stir in 2 cups coffee. Remove from heat. Set lamb back in pan (without rack); spoon juices over it. Cover tightly with foil.
Return to oven and cook until lamb is tender and pulling away from the bone, about 5 hours, turning lamb once halfway through cooking.
Transfer lamb to a platter and cover with foil. Reheat remaining 1 cup coffee and pour with liquid and vegetables from pan into a blender, working in batches if needed. Pulse until smooth. Pour sauce through a strainer set over a bowl, using the back of a spoon or ladle to push it through if needed. Season sauce with salt and pepper. Pour half of sauce over lamb and serve the rest in a bowl. Sprinkle lamb with parsley.
Note: Nutritional analysis is per serving.