Preheat the oven to 350°F.
Evenly season all sides of each short rib with salt and pepper. Set aside.
To an oven-safe Dutch oven over medium-high heat, add the olive oil. Once hot, sear each side of the ribs, working in batches if necessary. Transfer the seared ribs onto a plate and set aside.
Reduce heat to medium. To the Dutch oven, add the onions, tomato paste, and beer. Stir to combine, scraping the brown bits from the bottom of the Dutch oven as you go. Continue cooking for 5 more minutes to allow some of the alcohol to evaporate.
Add thyme, parsley, rosemary, broth, Worcestershire sauce, and the seared ribs.
Bring the mixture to a boil. Cover the Dutch oven and carefully transfer it to the oven. Cook for 3 hours, or until the meat is tender and starting to fall off the bone.
When done cooking, carefully remove the ribs and transfer them to a plate. Tent with aluminum foil to keep warm.
Discard the herbs from the pot and transfer the liquid broth to a large glass bowl. You should have about 6 cups of broth. Use a spoon to skim off and discard the top layer of fat that has floated to the surface.
Heat the original Dutch oven over medium heat. Add butter and heat until melted. Add flour, whisking until no lumps remain.
Slowly add the broth back to the pot, whisking continually. Heat the mixture until it reaches a simmer. Continue cooking until the mixture thickens enough to coat the back of a spoon (approximately 5 more minutes).
Serve the short ribs and gravy over mashed potatoes.