Preheat oven to 275.
Chop the lamb into 1 inch cubes and season with salt and pepper. In a dutch oven or heavy bottom pot with a little bit of oil, brown the lamb on high heat to get a nice color on it. Remove from pot.
Add in the onion and carrot and cook about 10 minutes to soften. Add in the mushrooms and garlic and cook another 3 minutes. Add in the tomato and gin, and return the lamb to the pot. Add in the rosemary and thyme. Bring to a simmer.
Put into the oven at 275 and cook for about 4 and a half to 5 hours, stirring every hour or so. Once the lamb starts shredding on its own and all the bigger fat chunks are gone, you know it is done. It should be deep red and very thick. Stir in the 1/2 cup of pecorino
When the sauce is about done, bring a pot of salted water to a boil. Drop in your fresh pasta and cook only about 4 to 5 minutes. If using store-bought, follow the directions on the package for cook time.
Once cooked, put the pasta directly into the sauce along with a big ladle of the pasta cooking water and stir well to coat and combine. Be somewhat gentle to not break the noodles, but if you made them thick and dried them well, they will be fairly resilient.
Serve with a handful of parsley and pecorino