1. Preheat oven to 350 degrees. Season the short ribs generously with salt and freshly cracked black pepper (about 3-4 tsp each for the whole 5 lbs).
2. In a large dutch oven, heat the oil over high heat. Once the oil is hot, carefully sear the short ribs on all sides. Be careful not to overcrowd your pot and do this in batches if needed. Once you have a golden brown sear on all sides, remove and set aside.
3. Once all short ribs are seared, turn off the heat. Allow the leftover oil in the dutch oven to cool down a bit (about 5 mins). Drain the leftover oil into a safe container, reserving about 2 tbsp of the oil in the dutch oven.
4. Over medium high heat, allow the oil to get hot again. Once hot, add in the onion and carrots. Cook for 8-10 mins. Add in the tomato paste and cook with the veggies for another 10 mins over medium high heat, stirring frequently so it doesn’t burn.
5. Keeping the heat where it is at, add about 1 cup of the red wine to the dutch oven, scraping any bits from the bottom. Allow the wine to almost fully cook out, you’ll have a thick paste with the veggies. Add another cup of wine and repeat the same process. Reduce the wine to about half.
6. Add in the beef stock and bring to a boil. Add short ribs back in along with the head of garlic and fresh herbs. Bring to a boil, cover and braise in the oven for 2-2.5 hours or until the short ribs are fork tender.