Preheat your oven to 300° F (150° C).
Place a Dutch oven or cast iron pot over high heat. When hot, add oil.
Season the short ribs liberally with salt and pepper. Place them in the pot and sear well on both sides. Transfer to a plate.
Add more oil to the skillet, then add the onion, celery, and carrot. Sear until they get good color, then add in the garlic, thyme, bay leaves, tomato paste, red wine, and stock. Bring to the boil and whisk any browned bits off the bottom. Then add the beef ribs back to the pot.
Cover with the lid or tin foil and place the pot in the oven for 3-3.5 hours. Check the meat; if it easily can be pulled from the bone, it’s done. Otherwise, continue cooking until it is.
Remove the pot from the oven. Transfer the ribs out of the pot. Also remove the bay leaves.
OPTIONAL STEP: Use an immersion blender to blend up the veggies in the sauce.
Strain the sauce through a fine mesh strainer and put it back into the cooking pot on the stovetop over medium heat. Bring it to a boil, then simmer. You can add some cornstarch slurry to thicken if necessary. Add the ribs back in and rotate them around in the sauce until they’re coated.
Serve on a bed of mashed potatoes with the sauce poured over. You can garnish with some red chilis and parsley, if you like.