Season the short ribs on all sides with 1 teaspoon salt and ½ teaspoon black pepper (reserve the rest for later).
Heat olive oil in a Dutch oven over medium-high heat.
Add the seasoned short ribs to the Dutch oven and sear on all sides, about 2 minutes per side.
Remove browned short ribs and transfer to a plate; set aside.
To the Dutch oven, add the onions, carrots, and celery. Stir, sautéing for 2-3 minutes, just until the vegetables are soft.
Add the garlic, stir, and sauté for 1 more minute.
Reduce the heat to medium. Add the tomato paste, flour, bay leaves, thyme, and rosemary. Stir to combine, then add the beef stock. Stir and deglaze the bottom of the pan with the wooden spoon, scraping up any browned bits.
Return the short ribs back to the pot on top of the vegetables.
Pour the beer over the ribs and stir just to loosen the veggies a bit. Turn off the heat on the stovetop.
Place the lid on the Dutch oven and place in the middle rack of the oven.
Cook in the oven for 2½ hours. The meat should be tender and falling off the bone.
Notes
Makes approximately 4-6 servings.Meat doneness: Meat is done when an internal thermometer inserted into the thickest part of the meat reads 145°F.Storage: allow the short ribs to cool, then store in an airtight container in the refrigerator for up to 4 days.