Bring the stock to a simmer in a small saucepan. Put the porcini in a spouted measuring cup, and add 1 cup of the hot stock. Season the beef all over with 1/2 teaspoon of the salt. Spread some flour on a plate, and lightly dredge the beef in the flour, tapping off the excess. Heat 3 tablespoons of the olive oil in a large Dutch oven over medium heat. When the oil is hot, add the beef and brown all over, about 8 minutes. Remove the beef chunks to a plate as they brown.

Once all of the beef is out, add the remaining 2 tablespoons olive oil to the Dutch oven. When the oil is hot, add the onion and carrot, and cook until the onion softens, about 6 minutes. Clear a space in the pan, and add the tomato paste. Cook and stir the tomato paste in that spot until it toasts and darkens a shade or two, about 2 minutes. Stir the tomato paste into the vegetables, and add the wine. Bring to a simmer, and cook until reduced by half, about 2 minutes. Add the bay leaves, cloves, and remaining teaspoon of salt. Remove the porcini from the soaking liquid and chop; add them to the pot. Pour the soaking liquid into the pot, leaving the grit behind in the bottom of the cup. Add the beef back to the pot, and ladle in enough of the hot stock just to cover the beef. Cover, and simmer until the beef is very tender and falling apart, about 1 1/2 to 2 hours, adding more stock as you go to maintain the level of liquid (if you run out of stock, add a little water). Remove the bay leaves.

When the beef is almost ready, bring a large pot of salted water to boil for the pasta. Add the pasta. Bring the beef and sauce to a boil, and cook a minute or two to thicken the sauce to your liking. When the pasta is al dente, remove with a spider directly to the sauce. Toss to coat the pasta with the sauce, adding a little pasta water if it seems dry. Remove the pot from the heat. Sprinkle with the grated cheese, toss, and serve.