Pat each veal shank completely dry with paper towels. Tie butcher’s twine around the circumference of each shank to hold its shape during cooking. Season generously on all sides with salt and pepper. Dredge lightly in flour, shaking off any excess.

Heat olive oil and 2 tablespoons of butter in a large Dutch oven over medium-high heat until shimmering. Working in batches of 2–3 shanks, sear each shank 4–5 minutes per side until deeply browned. Transfer to a plate and repeat. Do not rush this step.

Reduce heat to medium. Add the remaining 2 tablespoons butter to the same pot. Add onion, celery, and carrot. Cook, stirring occasionally, 8–10 minutes until softened and beginning to color. Add garlic and cook another 2 minutes.

Increase heat to medium-high. Pour in all the white wine at once. Use a wooden spoon to scrape up every browned bit from the bottom of the pot. Let the wine reduce by half, about 4–5 minutes.

Stir in the crushed tomatoes and demi-glace (or reduced stock). Add thyme and bay leaf. Nestle the seared shanks back into the pot — they should be partially submerged, liquid coming about two-thirds up the sides.

Cover tightly and transfer to a 350°F (175°C) oven. Braise for 1 hour 30 minutes to 2 hours, until the meat is very tender and pulling away from the bone. Check at 90 minutes — the meat should yield easily when tested with a fork but still hold its shape.

While the shanks rest, combine parsley, garlic, and lemon zest in a small bowl for the gremolata. Set aside.

Remove the shanks carefully and set on a warm plate. Discard the twine. Strain the braising liquid through a fine-mesh sieve into a saucepan, pressing on the solids. Simmer over medium heat until the sauce reduces to your desired consistency, 5–10 minutes. Taste and adjust seasoning.

Place each shank over risotto, polenta, or mashed potatoes. Spoon sauce generously over the top. Finish with a liberal scattering of gremolata. Serve immediately.