Sit short ribs out for about 15 minutes before you're ready to cook. Season liberally with salt and pepper.
Heat olive oil in large cast iron pot or dutch oven on high. Sear short ribs on each side to get a nice crust. Remove from pan. Cook in batches if needed to get a really good crust on each side.
Drain most of the fat, keeping a bit on the bottom. Add onion and carrot. Cook over medium high until softened.
Add garlic and sauté an additional 30 seconds or so until fragrant.
Add tomato paste and sauté until thick and begins to brown - 2 minutes or so.
Deglaze with wine, scraping up all the goodies at the bottom of the pan. Simmer to reduce, about 10 minutes.
Add remaining ingredients: tomatoes, stock, mustard, and herbs. Stir well.
Add meat back in, ensuring they are completely covered in sauce. Simmer on high heat for about 5 minutes. Reduce heat to low, cover, and simmer for 80-90 minutes until meat falls apart easily.
Remove meat once cooked and shred on cutting board. Clean up sauce by removing any bones that were in short ribs, as well as herb stems and bay leaves. Add shredded meat back to pot and continue simmering sauce about 20 minutes.
Serve with fresh pasta, a heaping scoop of gravy, and garnish with cheese and parsley or basil.