In a large skillet, heat 2 tablespoons of olive oil.
Add the beef and brown on both sides (about 5 minutes on each side).
While the meat is browning, chop the carrot, celery and onion.
Remove the meat from the skilled and place inside the slow cooker (or other oven pan).
Add the onion, celery, carrots to the skillet together with the garlic clove crushed, and the rosemary sprig.
Cook for about 5 minutes until softens.
Add the veggies in the slow cooker with the meat.
Add the red wine, broth and tomato paste.
Season with salt (about 2 teaspoons, you can taste and adjust later) and pepper, and stir.
Cover the pan, set on low and let it cook for 8 hours, until the meat is falling apart.
If you are not using a slow cooker, cover your oven pan tightly, add a couple of layers of aluminum foil to seal better, and bake at 350? for 3 hours. In this case you need to check the pan once in a while to see if it needs more liquid. Add some more beef broth if necessary..
About 40 minutes before the meat is ready, place the dry porcini in a bowl with hot water. Let them sit for 20 minutes.
Cut the meat using two forks in medium to small pieces based on how you like them best (I wouldn't shred the meat too small, it's nice to have some bigger pieces with the pasta).
Move them with some of the sauce to a skillet, add the porcini cut in pieces (and well drained) , and let them cook over medium heat for about 20 minutes. Let the sauce get a little denser, or add more if needed.
Bring a large pot of salted water to a boil. And cook the pasta following the instruction on the bag (it should take around 10 minutes for the pasta to cook al dente).
Drain the pasta and add to the skillet.
Toss well. Serve immediately topped with grated pecorino cheese if desired.