Preheat oven to 375 Fahrenheit. In a Dutch oven, heat oil over medium-high heat. Season the short ribs very generously with salt and pepper, brown all sides. Do in batches if needed, then remove to plate.
Add carrots, celery and onion, sauté for 3 minutes, then add garlic. Continue until onions are slightly translucent, then remove all to a plate.
Add ½ cup of broth to the pot and deglaze with a wooden spatula, scraping all the brown bits off the bottom. Reduce heat to low, season the potatoes with salt, and place them at the bottom in a single layer. Place the ribs on top, then spread the vegetables on and around the ribs. Add the beer and enough broth to cover the ingredients. Add thyme, brown sugar, tomato paste, and cognac. Increase the heat and bring to a small boil, stirring in the tomato paste gently.
Transfer to oven and cook on the middle rack for about 1.5-2 hours, until meat falls off the bone. Enjoy.