Place garlic cloves, onion, pepper, chili powder, thyme leaves, salt, olive oil and apple cider vinegar in a food processor and pulse until ingredients are finely chopped, not puréed. Score the fat on the pork diagonally with a sharp knife, and then create cuts all over the pork about 1/2 inch deep. This will allow the rub to infuse throughout the meat.
Rub the meat all over with all the ingredients and place the pork into a large crock pot, fat side up. Pour the white wine and beef broth into the bottom of the crock pot. Set the crock pot on low for 10 hours.
About an hour before serving the meat, prepare the pumpkin polenta. Pre-heat oven to 400 degrees F. On a sheet pan, place the pumpkin flesh side down and roast in the oven for about 45 minutes. Remove. When pumpkins are cool enough to handle, spoon the pumpkin flesh into a bowl and stir until smooth.
Bring 5 cups of water to a boil in a medium stockpot with the salt and pepper. Add the polenta to the boiling water and stir for about 2 minutes. Bring the water to a simmer and allow to cook, stirring often. When fully cooked (about 45 minutes - about the time the pumpkins are done) and smooth, whisk in butter, cheese, and pumpkin purée. Check seasonings and adjust as needed.
Remove pork to a cutting board to rest for about 15 minutes. Distribute polenta among 4 bowls. Carve the pork and place on top of each individual bowl of polent. Ssprinkle with parsley. Serve with a side salad and crusty bread.