3 teaspoons kosher salt, divided, plus more for seasoning
2 teaspoons cayenne pepper
2 teaspoons paprika
1 teaspoon freshly ground black pepper, plus more for seasoning
4 pounds beef short ribs (cut English-style, meaning meat on top of long bones—aka semi-Flintstone style—as opposed to cut across the bones)
6 tablespoons canola oil, divided
4 large carrots, cut crosswise into 2-inch pieces
3 stalks celery, cut crosswise into 2-inch pieces
1 (14.5-ounce) bag frozen pearl onions, defrosted (or 1 large onion, diced)
1 tablespoon tomato paste
1½ tablespoons flour
1 (12-ounce) bottle beer (any kind)
2 tablespoons light brown sugar
6 large Roma tomatoes, diced (about 3 cups, or two 14.5-ounce cans diced tomatoes in juice)
2 cups beef broth
2 bay leaves
Preheat the oven to 325°F. Combine 1 teaspoon of the salt with the cayenne, paprika, and pepper in a small bowl. Rub all of the meaty parts of the ribs with the rub. Heat 4 tablespoons of the oil in a large Dutch oven over medium-high heat, add the ribs and brown all over, about 8 minutes total. Transfer to a plate, drain and discard the liquid, then wipe out the pot with a paper towel (some of the spices in the pot may be a tad burnt and you don’t want that involved with the rest of the recipe).
Heat the remaining 2 tablespoons oil in the pot, then add the carrots, celery, and onions and cook until the celery and carrots begin to soften, 5 minutes. Stir in the tomato paste and cook for 1 minute. Add the flour and cook, stirring, until it disappears into the vegetables and the flour browns a drop, 1-2 minutes. Add the beer, scrape up the brown bits at the bottom of the pot, bring to a boil and cook until the liquid is reduced by half and thickened, 5-6 minutes.
Stir in the brown sugar, then add the tomatoes, beef broth, remaining 2 teaspoons salt, and bay leaves. Bring to a boil then add the short ribs, bone side up. Reduce to a simmer, then cover and transfer to the oven; braise until the meat is falling off the bone and the liquid has thickened, 2½ to 3 hours. Remove from the oven.
Using tongs, transfer the ribs from the liquid to a serving bowl and cover with foil to keep warm. Arrange a colander over a large bowl and dump the vegetables and liquid into the colander. Skim the fat off the liquid and season it with salt and pepper. Arrange the veggies on the serving platter with the short ribs and serve the cooking liquid on the side for drizzling, pouring, or dunking.