Brown the beef: Heat olive oil in a Dutch oven over medium-high heat. Sear the short ribs in batches if needed, browning each side well. Transfer the ribs to a plate.

Cook the vegetables: Reduce the heat to medium. Add onion, carrots, and celery to the same pot. Cook for 6–8 minutes until softened. Add garlic and cook for another minute.

Add tomato paste: Stir in the tomato paste and cook for 1–2 minutes until slightly darkened.

Deglaze with wine: Pour in the red wine and scrape the browned bits from the bottom of the pot. Simmer for 8–10 minutes until the wine reduces noticeably.

Start the braise: Add beef stock, thyme, rosemary, and bay leaves. Return the short ribs to the pot. Bring the liquid to a gentle simmer.

Braise the short ribs: Cover and place in a 325°F oven for about 2½–3 hours. The beef is ready when a fork slides into it easily and the meat pulls apart without much resistance.

Shred the beef: Remove the short ribs and let them cool slightly. Remove the bones and excess fat, then shred the meat into bite-sized pieces. Strain and reserve some of the braising liquid.

Make the Grana Padano crema: Warm the heavy cream over low heat. Add butter, then gradually whisk in the grated Grana Padano. Stir until smooth. Season with black pepper.

Prepare the gremolata: Combine parsley, horseradish, lemon zest, lemon juice, and a pinch of salt. Start with less horseradish and add more to taste.

Toast the breadcrumbs: Heat olive oil or butter in a small skillet. Add panko and cook until golden and crisp. Stir in parsley and Italian seasoning.

Cook the lumache: Cook the lumache in well-salted boiling water according to the package directions. Reserve at least 1 cup of pasta water before draining.

Combine the pasta and beef: Add cooked lumache to a large skillet with the shredded short rib, Grana Padano crema, and a splash of braising liquid. Toss over low heat.

Adjust the sauce: Add reserved pasta water a little at a time until the sauce becomes glossy and coats the pasta. Do not add all the water at once.

Finish and serve: Turn off the heat and fold in some arugula. Divide between bowls and finish with horseradish gremolata, herb breadcrumbs, extra Grana Padano, black pepper, and a small squeeze of lemon if desired.