Step 1: Sear the Beef Shanks : Pat beef shanks dry and season with salt and pepper. Heat olive oil in a Dutch oven and sear each shank for about 3–4 minutes per side until golden brown. Remove and set aside.
Step 2: Build the Flavor Base : In the same pot, add onion, carrots, and celery. Sauté until softened, then stir in minced garlic and tomato paste. Cook for 1–2 minutes to develop depth of flavor.
Step 3: Deglaze with Wine : Pour in red wine to deglaze the pan, scraping up browned bits. Simmer for 5 minutes until the wine reduces by half.
Step 4: Braise the Meat : Add beef broth, herbs, and balsamic vinegar. Return shanks to the pot, ensuring they are mostly submerged. Cover and simmer gently for 2 to 2½ hours until fork-tender.
Step 5: Prepare the Polenta : While the beef cooks, boil water or broth in a saucepan. Gradually whisk in cornmeal, reduce heat, and cook for about 20 minutes, stirring often, until smooth and creamy. Finish with butter, Parmesan, and salt.
Step 6: Finish the Dish : Once beef is tender, remove from the sauce. Reduce the sauce over medium heat until thickened. Serve beef shanks over creamy polenta and drizzle with the reduced sauce.