Preheat your oven to 425 degrees Make sure you have the center rack ready to go.
Line a sheet pan with aluminum foil and evenly place short ribs on pan. Brush each rib with olive oil and season with salt and pepper.
Place ribs on the center rack of the oven and roast for 25 minutes They should brown, cutting out a skillet browning step.
Using a large Dutch oven, heat olive oil on medium heat with 3 cloves of garlic, stirring frequently. Once the oil is hot and garlic is brown, remove garlic. Add chopped carrots, onions, leeks, and celery for about 15 minutes, until soft and veggies start to brown, add the mushrooms at this point. Stir in tomato paste and chopped garlic and cook for a minute, until softened and tomato paste cooks and mixes in with the veg. Warming the whole garlic cloves in the oil, helps flavor the oil for cooking the vegetables.
Add an entire bottle of your favorite red wine to the pot and bring to a boil.
Reduce the heat and simmer for about 10 minutes, allowing the wine to reduce. Add the stock, thyme, 1 tablespoon kosher salt, and 1 ½-2 teaspoons of black pepper.
Transfer the ribs to the pot and bring them back to a boil.
Cover with the lid and cook for an hour, uncovering and cooking for an additional hour, allowing the meat to get extremely tender.
Take the short ribs out of the pot and set them aside. Remove the thyme and bones that have separated and are loose. Uncover and simmer, allowing the red wine to thicken a little bit. As it simmers, remove some of the fat with a spoon. After about 20 minutes, put the ribs back in the pot for 5 more minutes to rewarm. Serve ribs and vegetables on a heap of mashed potatoes with some fresh bread to soak up the sauce.