In a large skillet, heat olive oil over medium-high heat. Add the ground lamb and brown it, breaking it into small chunks as it cooks.
Once the lamb is browned, add chopped onions, minced garlic, diced celery, and carrots to the skillet. Cook until the vegetables have softened, about 5-7 minutes.
Stir in the herbs and spices, including cayenne pepper, oregano, rosemary, thyme, cinnamon, cloves, and nutmeg. Cook for an additional minute to release the flavors.
Pour in the red wine to deglaze the pan, scraping up any browned bits from the bottom. Allow it to simmer for about 2-3 minutes.
Add the tomato sauce or paste and chicken broth to the pan. Reduce the heat and let the mixture simmer for 15-20 minutes to meld the flavors, stirring occasionally.
Meanwhile, cook the pasta according to package instructions. Drain and set aside.
Once the sauce has thickened, combine it with the cooked pasta in the skillet, tossing to ensure the pasta is well coated.
Serve hot, garnished with grated cheese and fresh herbs, alongside garlic bread or a salad if desired.