Pat the veal shanks very dry, tie each piece with kitchen twine if needed, then season both sides with salt and pepper.
Dust the shanks lightly with flour and shake off the excess so the crust browns instead of becoming pasty.
Heat olive oil and butter in a heavy Dutch oven over medium-high heat, then sear the shanks 3–4 minutes per side until deeply golden. Transfer to a plate.
Lower the heat to medium, add onion, carrot, and celery, and cook 6–8 minutes until softened and lightly sweet.
Stir in garlic and tomato paste, cooking 1–2 minutes until fragrant and brick-red.
Pour in white wine, scrape the browned bits from the pot, and simmer 3–4 minutes to reduce slightly.
Add stock, crushed tomatoes, bay leaves, and thyme, then return the shanks to the pot in a single layer.
Cover and braise gently on low heat for 1 hour 45 minutes to 2 hours, turning once, until the meat is tender but still holding its shape.
While the meat finishes, simmer milk and water, whisk in polenta, cook gently 25–30 minutes, then stir in butter, Parmesan, and salt until creamy.
Mix parsley, lemon zest, and grated garlic for the gremolata; spoon polenta onto plates, top with osso buco and sauce, then garnish just before serving.
Dish type
Secondo / Main course