Begin by preheating your oven to 325°F (163°C). Pat the short ribs dry and generously season them with salt and pepper on all sides.
In a large Dutch oven, heat olive oil over medium-high heat. Sear the short ribs for about 12 minutes, turning until they develop a rich brown crust. Remove from the pot and set aside.
Add the diced onion, carrots, and chopped celery to the pot. Sauté for approximately 6 minutes or until softened. Then, include the minced garlic, thyme, rosemary, and bay leaves, cooking for another minute.
Stir in the tomato paste and let it cook for 2 minutes, allowing the flavors to deepen. Then pour in the red wine and Worcestershire sauce, stirring to lift the browned bits from the bottom of the pot. Let the mixture reduce by half for about 10 minutes.
Return the short ribs to the pot, add the beef stock until the ribs are covered, and bring to a gentle simmer.
Cover the pot and place it in the oven. Braise for 2.5 to 3 hours, or until the ribs are tender and fall apart easily.
While the ribs are cooking, prepare the creamy polenta. In a saucepan, combine chicken broth and milk, bringing it to a gentle simmer. Gradually whisk in the polenta, stirring occasionally for 30 to 40 minutes until creamy. Add butter and Parmesan, season with salt and pepper to taste.
In the final 20 minutes of cooking for the ribs, sauté the mushrooms in a skillet with a bit of olive oil, salt, and pepper until golden brown. Stir these into the pot with the short ribs as they finish cooking.
After removing the pot from the oven, discard the herb stems and bay leaves. If desired, thicken the sauce on the stove for a few minutes. Serve the short ribs hot over the polenta and garnish with fresh parsley.