On a cutting board, cut the rabbit into 9 pieces with game shears. Cut the saddle (center portion) into 3 pieces. Cut the front portion (front legs) in half through the backbone. Chop each hind leg into 2 pieces.
Season the meat with 1 teaspoon each of the salt and black pepper.
Heat the oil in a Dutch oven. When hot, add the rabbit, brown on both side for about 3 minutes each, then remove from the pot and set aside.
Add the bacon and onion to the pot and cook for about 5 minutes until onions soft. Add the garlic and rosemary and cook another 2 minutes.
Return the rabbit back into the pot. Add chicken broth and stir everything together. Place the lid on the Dutch oven and transfer it to the oven to cook at 325 degrees F for about 1 hour until rabbit is very tender.
Remove the Dutch oven from the heat, then remove the rabbit pieces from the pot and transfer to a large platter or cutting board. Let the meat cool for about 10 minutes until safe to handle, then shred the meat using 2 forks. Be careful to remove and discard all the small bones.
Transfer all of the liquid and remaining contents in the Dutch oven to a large bowl and save for a nice bowl of rabbit soup later in the week.
Use paper towels to wipe out the Dutch oven and then return to the stovetop over medium high heat and add the mushrooms. Do not move the mushrooms until they have caramelized on the bottom. If you toss them too soon, they will release their liquid and begin to steam. When the bottoms are caramelized, toss them and continue to cook for about 3 minutes.
Add the butter. Cook and toss for 1 minute. Push the mushrooms to one side making room for the polenta. Fry each slice of polenta for 2 minutes on each side until golden brown. Meanwhile, cook and toss mushrooms until beautifully browned. The polenta and mushrooms should be done at the same time.
Transfer two slices of polenta to each plate, season with salt and pepper, then top with cooked rabbit meat and mushrooms. Garnish each plate with 1 tablespoon each chopped parsley and Parmesan cheese and drizzle with olive oil. Serve immediately.