Prepared in 30 minutes or less plus 1½ hours to simmer.
In a large casserole or Dutch oven, heat oil on high heat. Season lamb cubes with salt and fresh pepper and add to hot casserole pan. Sear the lamb cubes on all sides until browned.
Remove browned lamb and place on a plate and set aside. Add the celery, carrot, garlic and thyme sprigs into casserole over medium heat and cook for 5 -7 minutes until tender and browned.
Stir in the red wine and peeled tomatoes, scraping bottom of casserole as you cook vegetables.
Bring to a boil and return lamb cubes to casserole pan. Reduce heat and simmer over low heat, covered, for 1½ hours. Remove meat and allow to cool completely so you can shred it with a sharp fork.
Remove thyme sprigs and discard. Return shredded lamb to casserole pan, add olives and simmer on low heat for 30 minutes.
The mixture should now resemble a thick ragu. Season with salt and pepper to taste.
Bring six quarts of unsalted water to boil. Add tagliatelle pasta and cook according to package. Drain pasta in a colander reserving a cup of the hot pasta water.
Add pasta to casserole pan and a touch of the hot pasta water then toss over high heat for a minute. Drizzle with olive oil then divide among four pasta bowls.
Garnish with grated Parmigiano-Reggiano cheese and chopped parsley. Serve immediately. Serves 4.
