How to Make It
Preheat the oven to 325°. In a large enameled cast-iron casserole, heat the oil until shimmering. Season the short ribs with salt and pepper and add 3 of them to the casserole. Cook over moderate heat, turning, until well browned all over, about 10 minutes. Transfer to a plate and repeat with the remaining ribs.
Pour off all but 2 tablespoons of the fat from the casserole. Add the onion and carrot and cook over moderate heat, stirring occasionally, until the vegetables are softened, about 8 minutes. Add the beef stock and beer and bring to a boil. Return the ribs to the casserole, cover and braise in the oven for about 2 hours, until the meat is very tender.
Transfer the ribs to a platter and tent with foil. Using a slotted spoon, transfer the vegetables to a blender. Strain the sauce into a heatproof measuring cup and skim off the fat. Add the sauce to the blender and puree until smooth. Return the sauce to the casserole and boil until reduced to 3 cups, about 8 minutes. Season with salt and pepper. Return the short ribs to the sauce and simmer over low heat until they are warmed through. Serve the ribs with the grits.