Preheat oven to 300ºF.

Season short ribs with the salt and pepper.

Heat the cooking fat in a large roasting pan or shallow Dutch oven over medium-high heat. Brown short ribs for about 5 minutes per side, until well browned, working in 2 batches to avoid crowding the pan. Transfer short ribs to a dish and set aside.

To the pan, add the carrots, celery and onion. Sauté for 5 minutes, until onions are softened and translucent. Add the garlic and rosemary and sauté 1 more minute, until the garlic and rosemary are coated in the cooking fat.

Add the beer. Use a wooden spoon or spatula to nudge the browned bits from the bottom of the pan, then bring up to a simmer and let simmer for 5 minutes, until reduced by about a third. Stir in the broth, mustard and tomato paste.

Add the ribs back to the pan, along with any juices that have run out onto the dish. Nestle the ribs in with the vegetables and braising liquid, in a single layer. Cover the pan with aluminum foil (if using a Dutch oven, put on the lid).

Place the covered pan in the oven for 2 hours, then uncover the pan and let cook, uncovered, for a final 30 minutes.

Remove the pan from the oven. Check to see that the meat is fall-apart tender. Discard the rosemary. Serve directly from the cooking pan or gently transfer the ribs to a platter or individual serving plates, spooning some of the cooking liquid and vegetables over the ribs.

Serve hot, with smashed rutabaga (or mashed potatoes or polenta).