6 to 8 meaty beef short ribs (bone-in, about 3 to 4 pounds)
1/4 teaspoon kosher salt (or more, to taste)
1/4 teaspoon freshly ground black pepper (or more, to taste)
2 tablespoons vegetable oil
1 cup diced celery
1 cup diced or sliced carrots
1 1/2 cups chopped onion
4 cloves garlic (sliced)
2 cups dry red wine (e.g., Cabernet, Malbec, or Merlot)
1 1/2 cups chicken stock (unsalted, or use veal or beef stock)
1/2 teaspoon dried thyme
Sprinkle the short ribs with salt and pepper.
Heat the vegetable oil in a large skillet or sauté pan over medium heat. Add the short ribs and cook for about 10 minutes, turning to brown all sides. Remove to the slow cooker insert.
Add the celery, carrots, onion, and garlic to the same skillet. Cook over medium heat, stirring frequently until lightly browned, about 8 to 10 minutes. Add the red wine, the veal or chicken broth, and the thyme. Bring the mixture to a full boil.
Pour the hot wine and vegetable mixture over the short ribs in the slow cooker. Cover and cook on low for 6 to 8 hours, until the meat is very tender. Alternatively, cook them on high for about 3 to 5 hours.
Remove the short ribs to a serving bowl or platter and keep warm. At this point they will have separated from the bones, so you can discard the bones.
Strain the cooking liquids and discard the solids. Skim fat from the juices (use a gravy separator if possible). Add the juices to a medium saucepan. Bring to a full boil over high heat. Reduce heat to medium and continue boiling for about 5 minutes, or until reduced by about one-third to one-half. You should have about 2 cups of sauce. Taste the sauce and season with salt and freshly ground pepper, as needed.
Pour the sauce over the short ribs and serve immediately, or return to the slow cooker and keep warm until serving time. Serve with mashed potatoes, potato gratin, or polenta.