Arrange the oven rack to the middle position. Preheat the oven to 425 °F (218°C). Place a wire rack on a baking sheet and set it aside.
Mix paprika, curry powder, ground cumin, salt, pepper, and dark brown sugar in a small bowl.
Pat dry the bone in short ribs on all sides using a sheet of paper towel.
Sprinkle them with the seasoning mixture on all sides.
Transfer them onto the wire rack and transfer to the preheated oven. Roast for 15 minutes. Take them out of the oven and set them aside while you are working on the rest of the ingredients.
Decrease the oven temperature to 350 °F (177 °C.)
Heat olive oil in a large (6-7 quart) Dutch oven over medium-high heat. Add the onion, carrots, and celery. Cook, stirring frequently, for 10 minutes or until vegetables are softened.
Add the garlic and cook for another 30 seconds scraping the bottom of the pot with a wooden spoon.
Add the bay leaf, beef stock, beer, and diced tomatoes into the pot. Turn the heat to medium-high and bring it to a boil. This takes about 15 minutes.
Off the heat, nestle the short ribs in the liquid. Cover it with a lid, transfer it to the oven, and cook for 2 hours, removing the lid in the last 30 minutes of cooking. At the end of the cooking time, the meat should be falling off the bone tender.
Serve braised beef short ribs over rice, mashed potatoes, or polenta with a spoonful of the braising liquid and some of the vegetables.