5 pounds bone-in short ribs, at least 1 1/2 inches thick
Kosher salt and freshly ground pepper
2 large heads garlic, halved crosswise
1 medium onion (about 10 ounces), chopped
4 ribs celery (about 8 ounces, chopped
2 medium carrots (about 6 ounces), chopped
3 tablespoons tomato paste
2 cups dry red wine (about half a bottle)
2 cups beef stock or bone broth (use beef bouillon dissolved in water if unavailable; chicken stock will work in a pinch), plus more as needed
4 sprigs thyme
1 cup parsley, coarsely chopped
½ cup finely chopped chives
1 tablespoon finely grated lemon zest
Heat oven to 275 degrees. Heat oil in a large Dutch oven over medium-high heat. Season short ribs on all sides with salt and pepper. Working in batches, sear short ribs on all sides until deeply and evenly browned, 6 to 8 minutes per batch. Transfer browned short ribs to a large plate and continue with remaining ribs.
Pour off all but 2 tablespoons of remaining fat, leaving the good browned bits behind. Reduce heat to medium, and add garlic, cut side down and cook, undisturbed, until golden brown, about 1 to 2 minutes. Add onion, celery and carrots and season with salt and pepper. Toss to coat and continue to cook until vegetables are softened but not yet browned, about 5 to 10 minutes. Add tomato paste and stir to coat. Continue to cook, stirring occasionally, until tomato paste has started to caramelize a bit on the bottom and up the edges of the pot, about 2 to 3 minutes.
Add red wine and, using a wooden spoon, scrape up any browned or caramelized bits. Let this simmer 2 to 3 minutes, just to take the edge off and reduce a bit. Stir in beef stock along with thyme. Using tongs, return short ribs to the pot, along with any juices that have accumulated, nestling them in there so that they are submerged (if they are just barely covered, nestle them bone side up so that all the meat is submerged, adding more beef stock or water as necessary to cover). Bring to a simmer, then cover and transfer to oven.
Cook, undisturbed, until short ribs are meltingly tender and falling off the bone (you should be able to shred the meat with a fork), 3½ to 4 hours.
Using tongs, remove the ribs from the pot, taking care (for presentation purposes, really) not to let the bone slip out and transfer them to a large plate. (While you could serve the short ribs right out of this pot, the vegetables have all given up their flavor and texture and aren’t worth much now, so feel free to strain the sauce for easier eating.) Scatter parsley, chives and lemon zest over the top of the short ribs. Separate the fat from the sauce, season with salt and pepper and serve alongside.