Preheat the oven: Preheat oven to 325°F.
Season the ribs: Pat the short ribs completely dry. Season generously with salt and black pepper.
Sear the ribs: Heat the olive oil in a large Dutch oven over medium-high heat. Sear the short ribs for 2–3 minutes per side, until deeply browned. Work in batches if needed so the pan isn't crowded. Remove the ribs and set aside.
Cook the vegetables: Add the onion and carrots to the same pot and cook for 5–7 minutes, scraping up the browned bits from the bottom. Add the garlic and cook for another minute.
Add the tomato paste: Stir in the tomato paste and cook for 1–2 minutes, until it darkens slightly and begins to caramelize.
Deglaze: Pour in the red wine and scrape up everything from the bottom of the pot. Simmer for about 5 minutes, until the wine has reduced slightly.
Make the braising sauce: Add the bone broth, balsamic vinegar, soy sauce, Worcestershire sauce, and honey. Stir until combined. Add the rosemary and thyme.
Braise: Return the short ribs to the pot. The liquid should reach about halfway to two-thirds of the way up the meat. Bring to a gentle simmer, cover tightly, and transfer to the oven. Braise for 3–3½ hours, until the meat is extremely tender and easily pulls away from the bone.
Make the sauce: Remove the short ribs and discard the rosemary and thyme stems. Skim excess fat from the braising liquid. Use an immersion blender to blend the onions and carrots directly into the braising liquid until smooth. Simmer uncovered on the stovetop for 10–15 minutes, until the sauce is rich and thick enough to coat the back of a spoon. Taste before adding anything else. Add more salt, pepper, balsamic, honey, or soy sauce if needed.
Make the Parmesan polenta: Bring the bone broth to a gentle boil. Slowly whisk in the polenta, then reduce the heat to low. Cook according to package directions, stirring frequently, until thick and creamy. Stir in the butter, heavy cream, and Parmesan. Season with salt and black pepper. Add a splash of bone broth or cream if the polenta gets too thick.
Serve: Spoon the creamy Parmesan polenta into shallow bowls. Place the short ribs over the polenta and generously spoon the balsamic-honey braising sauce over everything. Finish with freshly cracked black pepper and fresh thyme or rosemary.