Preheat the oven to 325°F (163°C).
Pat the beef short ribs dry with paper towels. Season all sides evenly with kosher salt and freshly ground black pepper.
Heat the vegetable oil in a large Dutch oven or heavy oven-safe pot over medium-high heat.
Add the short ribs in batches, browning them on all sides for about 3-4 minutes per side. Remove the browned ribs and set aside.
Add the diced onion, carrots, and celery to the pot. Cook, stirring occasionally, until the vegetables soften and begin to brown, about 8-10 minutes.
Add the minced garlic and tomato paste to the vegetables. Stir and cook for 1-2 minutes until fragrant.
Pour in the red wine, scraping the bottom of the pot with a wooden spoon to release any browned bits. Bring to a simmer and cook until the wine is reduced by half, about 10 minutes.
Return the browned short ribs to the pot. Add the beef broth, fresh thyme, fresh rosemary, and bay leaves. The liquid should partially cover the ribs.
Bring the mixture to a simmer on the stovetop, then cover the pot with a tight-fitting lid and transfer it to the preheated oven.
Braise the short ribs in the oven for 3 to 3 ½ hours, or until the meat is very tender and falling off the bone.
Remove the pot from the oven. Carefully transfer the short ribs to a serving platter and cover loosely with foil to keep warm.
Discard the bay leaves and herb stems from the braising liquid. Skim off any excess fat from the surface.
Optionally, simmer the braising liquid on the stovetop over medium heat to reduce and thicken the sauce to your desired consistency, about 10 minutes.
Serve the braised short ribs hot, spooning the sauce and vegetables over the top.