Pat the short ribs dry with paper towels. Generously season all sides with salt and pepper.

Heat olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Brown ribs in batches, 3–4 minutes per side, until nicely caramelized.

Transfer ribs to a plate and set aside.

Reduce heat to medium. Add butter (or more oil) to the pot, then add the chopped onion, carrots, and celery. Cook until softened and starting to brown, about 6–8 minutes.

Stir in garlic and tomato paste; cook for 1 minute.

Pour in the red wine (or additional beef stock if skipping wine). Scrape up browned bits from the bottom of the pot. Let the wine reduce by about half, 3–5 minutes.

Return short ribs to the pot. Add beef stock, Worcestershire sauce, Dijon mustard, rosemary, thyme, and bay leaves. Ensure the liquid covers the ribs halfway.

Bring to a gentle simmer, cover, and transfer to a 325°F (160°C) oven. Cook for 2.5–3 hours, until the meat is tender.

Alternatively, simmer on the stovetop over very low heat.

Carefully remove ribs and keep warm. Strain the braising liquid into a saucepan. Skim fat, if desired.

Reduce the liquid over medium-high heat until concentrated. Stir in heavy cream and simmer until the sauce coats the back of a spoon.

For a thicker sauce, whisk flour with a splash of cold water and stir into the sauce. Adjust salt and pepper to taste.

Spoon creamy herb sauce onto a base of mashed potatoes or polenta, nestle a short rib on top, and spoon more sauce over the meat.

Garnish with extra herbs.