Preheat the oven to 325 degrees F.
Heat a dutch oven over high heat.
As the pan gets hot, lay the meat on a paper towel, and dry it sufficiently with another paper towel. Season with salt and pepper on both sides.
Season the dutch oven with some oil and wait for it to shimmer. It shouldn't be smoky, but a little whisper of smoke is fine.
Add the dried-off meat to the pan and sear until golden brown on all sides, about 2-3 minutes per side. You do not want to overcook the meat, so watch it closely and remove once it's caramelized. Transfer the short ribs to a plate. Pour out all but 2 tablespoons of drippings. Make sure all golden brown bits (AKA fond) are still on the bottom of the pot. Incase you're curious: you don't want this to be fat, oily overload, so that's why you're getting rid of any excess drippings that would overpower the dish.
Reduce the heat to medium and add the onion. Sauté until slightly softened and caramelized, about 5 minutes. Then, add the celery and garlic. Season with a generous pinch of salt. Sauté for another 2-3 minutes until the garlic is fragrant and the celery and slightly tender.
Add the red wine, pomegranate juice and beef broth. Use a wooden spoon to scrape the browned bits off the bottom of the pan, so it combines with the liquid. Bring the liquid to a boil, then reduce the heat to let it simmer for 3-4 minutes.
Reduce the heat to low. Add the rosemary and a bay leaf. Then, add the meat back into the mixture and submerge it as much as possible into the liquid. If more than the top of the short ribs are not covered by liquid, feel free to add more beef broth until they are fully covered. If making bone-in short ribs, place the meat down, so the bone is facing up. Once the meat is submerged, place the lid onto the dutch oven.
Transfer the dutch oven to your preheated oven and let them cook for 3 1/2 hours. Remove them from the heat after 3 hours and if they easily fall apart when touched with a fork, then they are done. If they don't, put them back in the oven for another 30 minutes or so.
Once the short ribs are done, remove them from the heat and serve! They will stay warm and tender in the dutch oven for up to 45 minutes. If you want to serve with the roasted carrots, recipe is below.