Preheat your oven to 325°F (163°C). Remove short ribs from the refrigerator 20–30 minutes before cooking, then pat all sides completely dry with paper towels and season generously with 2 tsp kosher salt and 1 tsp black pepper.
Heat 2 tbsp oil in a Dutch oven over medium-high until shimmering. Working in batches, sear the ribs on all sides for 3–4 minutes per side until deeply browned, then transfer to a plate and remove excess fat, leaving about 2 tbsp drippings.
Reduce heat to medium and cook the onion, carrots, and celery in the drippings for 5–7 minutes, scraping up browned bits. Add the smashed garlic and cook 1–2 minutes, then stir in the tomato paste and cook for 2 more minutes until it darkens slightly.
Pour in the red wine and scrape the bottom of the pot vigorously; bring to a boil and cook for 3–4 minutes. Add the beef bone broth, Worcestershire sauce, rosemary, thyme, and bay leaves; stir to combine.
Nestle the seared short ribs back into the pot bone-side up; the liquid should reach halfway up the sides of the ribs — add more stock if needed. Bring to a simmer, cover tightly, and transfer to the preheated 325°F oven.
Braise for 3 to 3.5 hours until the meat is completely fork-tender, falling off the bone, and slides easily when probed with a fork. If the ribs need more time, continue braising covered in 20-minute increments.
Remove ribs to a plate, discard herbs, and strain the braising liquid through a fine mesh strainer into a saucepan; skim fat thoroughly. Bring to a boil over medium-high heat and reduce for 10–15 minutes until glossy and sauce-like, then remove from heat and stir in 1 tbsp cold butter.
Taste the sauce and adjust seasoning with salt and pepper. Spoon the sauce over the short ribs and serve immediately over creamy mashed potatoes, egg noodles, or polenta, garnished with fresh thyme or rosemary if desired.