Preheat oven to 300°F (150°C)
Pat beef short ribs dry
Season generously with salt and black pepper
Heat a heavy pot or Dutch oven over medium-high heat
Add a small amount of oil
Sear short ribs in batches (2–4 minutes per side) until well browned
Remove ribs to a plate
Reduce heat to medium
Add chopped onion, carrots, and celery (optional) and cook 5–8 minutes
Add minced garlic (1–2 minutes)
Stir in tomato paste (1–2 minutes, optional)
Deglaze with red wine or beef broth, scraping browned bits
Add beef broth or stock to partially cover the ribs (about halfway)
Add aromatics (bay leaf, thyme, rosemary, or peppercorns)
Cover and braise in the oven 2.5–3.5 hours, until fork-tender
Check liquid level every 45–60 minutes; add more broth if needed
Remove ribs to a serving dish
Strain braising liquid (optional)
Skim fat from the surface (optional)
Reduce braising liquid on the stove 10–20 minutes to thicken
Return ribs to sauce to warm 5–10 minutes, or serve with sauce
Rest ribs 10–15 minutes before serving
Serve with mashed potatoes, polenta, rice, or crusty bread