In a large dutch oven (with a lid) or heavy bottomed pot, add the oil and place it on medium high heat. Season all sides of your short ribs with salt and pepper, then dredge each short rib with flour on all sides and place them directly into the pot, meat side down. Brown all sides of the short ribs and set them aside on a plate.
Add in the onions, carrots, celery, mushrooms and garlic, season with salt (just a little) and pepper, let them cook down for about 5 minutes, then add in the tomato paste and red wine. Let this cook down for about 5 minutes and then add in the beef broth along with the thyme. Place all your short ribs back in to the pot, submerging them into the broth as best as possible. Cover and let this cook for 2 ½ to 3 hours on the stove or in an oven at about 350F.
Once the short ribs have about 20 minutes left, begin working on the polenta by placing the chicken broth, milk and heavy cream (if using) into a medium size pan. Bring it to a light boil then down to a simmer. Add in the polenta and keep stirring to avoid any clumps. Cook for about 15-20 minutes stirring frequently. Once the polenta Is fully cooked and creamy, turn off the heat and add in the butter, Parmigiano Reggiano, and salt and pepper if needed. At this point, the short ribs should be ready. Use a spoon to remove all the excess fat that has risen to the top of the pot. Serve with the polenta and Enjoy/Sahtein!