Adding wine-steeped pasta to the leftover wine-braised beef ragu is super-intense.
Heat the extra-virgin olive oil in Dutch oven over medium-high heat, add the carrots, onions, celery, garlic and season with salt, and pepper. Cook until very tender, then stir in the tomato paste, stock, short rib meat, and braising sauce. Heat through, then cool completely and store for make-ahead meal. Skim the fat and reheat, covered, over medium heat.
While the sauce reheats, bring 5 to 6 cups of water to a boil with 1 bottle red wine. Add the pasta and cook to al dente. Drain the pasta and toss with sauce to coat, then top with Pecorino cheese and chopped parsley.