Preheat your oven to 375°F (190°C).
Preheat a large Dutch oven over medium to medium-high heat.
Season and sear the ribs: Brush short ribs with oil and season generously with salt and pepper on all sides. Sear in batches for about 2 minutes per side until well-browned. Transfer to a tray and set aside.
Sauté the vegetables: In the same pot, add onions, garlic, carrots, and celery. Scrape up the fond from the bottom of the pot. Season with 1 tbsp salt and ½ tsp pepper. Cook for 10–15 minutes, stirring occasionally, until softened and fragrant.
Build the braising liquid: Stir in crushed tomatoes and tomato paste. Cook for 3 minutes. Add the red wine and simmer to reduce by about half, around 5–10 minutes.
Add stock and herbs: Pour in beef stock and nestle in the thyme bundle. Let it come to a gentle simmer.
Return ribs to pot: Place the seared short ribs into the braising liquid. Cover and transfer to the oven. Braise for 2½ hours.
Uncover and finish: Remove the lid or foil and continue cooking uncovered for 30 minutes, until the meat is fall-apart tender.
Strain and reduce sauce: Remove the ribs and thyme bundle. Blend the sauce with an immersion blender for a smoother consistency. Simmer on medium heat to reduce to desired thickness. Taste and adjust seasoning.
Serve: Plate with potato purée and roasted vegetables. Spoon the red wine au jus over the top.