In a large, heavy-bottomed pot or Dutch oven, heat olive oil over medium heat. Add chopped onion, carrots, and celery. Sauté for about 8-10 minutes, stirring occasionally, until the vegetables are softened and the onions are translucent.

Push the vegetables to one side of the pot and add the cubed lamb. Season generously with salt and pepper. Brown the lamb on all sides, about 5-7 minutes.

Add minced garlic, chopped fresh rosemary, dried oregano, and red pepper flakes (if using) to the pot. Cook for another minute until fragrant. Stir everything together.

Pour in the red wine, scraping up any browned bits from the bottom of the pot. Let the wine simmer for 2-3 minutes.

Add the can of crushed tomatoes and beef broth to the pot. Stir well. Bring to a simmer, then reduce heat to low, cover, and simmer gently for at least 2-3 hours.

After simmering, check the lamb for tenderness. Once tender, use two forks to shred the lamb directly in the pot. Stir the shredded lamb back into the sauce.

Taste the ragu and adjust seasoning with salt and pepper. Simmer uncovered for another 15-20 minutes to thicken slightly if needed.

While the ragu is finishing, cook pasta according to package directions until al dente. Reserve about 1 cup of pasta water before draining.

Add cooked pasta to the pot with the ragu. Toss to coat, adding pasta water if needed. Serve immediately, garnished with Pecorino Romano cheese if desired.