Season and set aside the short ribs: Place the short ribs on a big platter or dish and liberally season both sides with salt and pepper. Give the short ribs at least 30 minutes to rest and acclimate to room temperature. Then, set the oven temperature to 325°F.
Brown the short ribs:To brown the short ribs, place the butter and olive oil in a large Dutch oven (at least five quarts in size and oven-safe) and heat it over medium-high heat. When the mixture begins to shimmer, carefully rotate the pot to coat the bottom equally. Working in batches, add a few short ribs to the pot being cautious not to overcrowd. The short ribs should be seared for two to three minutes on each side, or until a deep brown crust forms. Once all of the short ribs are browned, transfer them to a clean plate or small baking sheet and continue cooking, adding a little extra oil to the saucepan only as needed. After that, turn down the heat to medium and set the browned short ribs aside.
Sauté the mirepoix: Add the diced onion, celery, and carrot to the saucepan and sauté the mirepoix. The mixture should be sautéed, stirring occasionally. To taste, add salt or pepper to the mirepoix. Cook the vegetables for a further 10 to 15 minutes, or until they are soft, aromatic, and golden brown. Again, just add additional oil to the saucepan as needed if the mirepoix seems dry during sautéing.
Combining the flavors: After dusting the mirepoix mixture with flour, swirl to coat. Cook for one to two minutes, or until the flour disappears and starts to get a light brown color. Make a little indentation in the middle of the saucepan and pour in the tomato paste. After about two minutes, stir in the paste and mirepoix to coat. Next, include the Worcestershire sauce and utilize a wooden spoon to remove any caramelized residue from the pot's bottom. Stir to thoroughly mix in the chipotle powder, smoked paprika, dried oregano, and brown sugar.
Put together the braise: Put the short ribs that have browned back into the saucepan, along with any remaining liquids that have accumulated. Pour in the red wine and beef broth until the ribs are nearly fully covered. Place the fresh herbs, garlic head, and bay leaves into the saucepan and whisk everything together with care. After turning the heat up to medium-high and simmering the pot for about ten minutes, remove from the burner.
Braise the short ribs: To braise the short ribs, put a cover on the saucepan and place it in the oven. Cover and braise the short ribs for 3 to 3 1/2 hours, or until they are falling off the bone tender.
Adjust braising liquid, if needed: If necessary, adjust the braising liquid. Carefully remove the saucepan from the oven. Take out the garlic head, herb stems, and bay leaves from the saucepan. If necessary, skim any fat from the liquid's surface. If you want to thicken the braising liquid, heat the pot on the stovetop over medium-high heat. Cook for a little while, stirring gently, until the liquid achieves the consistency you want. After that, taste and add extra salt or pepper to suit.
Serve these short ribs with a red wine braison right away. I enjoy placing these short ribs in shallow bowls and covering them with a small amount of the braising sauce and creamy mashed potatoes. Have fun!