Preheat the oven to 160°C (320°F). Cut the beef short ribs into individual pieces, then dust them evenly with all-purpose flour. Heat 1 tablespoon of olive oil in a large flameproof casserole dish or Dutch oven over medium-high heat. In batches, fry the ribs until they are well browned on all sides, adding extra olive oil if needed. Transfer the browned ribs to a plate and set aside.
Add the diced speck, chopped carrot, quartered brown onions, and halved mushrooms to the same pot. Cook over medium heat, stirring frequently, until the vegetables begin to soften and the speck releases some of its fat.
Add the tomato paste and minced garlic to the softened vegetables and speck in the pot. Stir well and cook for about 30 seconds to allow the flavors to develop. Next, pour in the dark ale or porter and bring the mixture to a gentle simmer, scraping any browned bits from the bottom of the pot.
Stir in the wholegrain mustard, fresh thyme leaves, and fresh rosemary. Pour in the beef stock and mix everything thoroughly, making sure to scrape up all flavorful bits stuck to the bottom. Return the browned ribs (with any accumulated juices) to the pot. Gently bring the mixture back to a simmer.
Cover the pot with a lid and transfer to the preheated oven. Bake for about 2 hours, or until the beef is tender and falling off the bone. Once the braising time is up, taste and season the stew generously with freshly ground pepper and salt. I like to adjust the seasoning right at the end to bring out the best flavor in the sauce.