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.
If you weren’t already sure about how easy and delicious braised short ribs can be, consider this classic and straightforward recipe an excellent gateway. The ultimate hands-off, do-ahead dinner, these are done on the stovetop in a large Dutch oven but can easily be adapted to a slow cooker if that’s your thing. When purchasing the ribs, ask for the thickest, meatiest ones available as they tend to shrink quite a bit once braised.