Heat oven to 350 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 of 3-4 pieces, 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 oil in the pan. Reduce heat to medium, and add garlic, cut side down and cook, undisturbed, until golden brown, about 1 to 2 minutes. Add onion, celery, carrots, and jalapeño and season with salt, pepper, and smoked paprika. Mix well 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, about 2 to 3 minutes.
Add red wine and, using a wooden spoon, scrape up any browned or caramelized bits. Bring to a boil; lower heat to medium and simmer until wine is reduced by half, about 20 minutes. Stir in beef stock along with thyme, parsley, and rosemary. Using tongs, return short ribs to the pot, placing them in 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), 2½ to 3 hours.
Using tongs, remove the ribs from the pot, taking care not to let the bone slip out and transfer them to a large plate. Strain the vegetables from the sauce. (The vegetables no longer have flavor and can be discarded) Garnish with parsley, garlic and lemon zest over the top of the short ribs. Separate the fat from the sauce, season with salt and pepper and serve alongside.