This recipe is from Ethan Chlebowski's Youtube cooking channel. It really explains the method and the outcome is superb.
https://www.ethanchlebowski.com/cooking-techniques-recipes/red-wine-braised-short-ribs-1
INGREDIENTS
5 English Cut Short Ribs
Salt
30 g oil
1/2 white onion, rough dice
1 carrot, rough dice
1 stalk of celery, rough dice
30 g tomato paste
500 ml red wine
200 ml beef / veal stock (or plain water or more wine)
2 bay leaves
*** I cooked 8 ribs, a whole yellow onion, 2 carrots, 2 celery stalks, about a half small can of tomato paste, 1 can of Campbell’s beef broth, about 3 cups of water, only a half bottle of red wine (Italian, ie. dry) because I didn't want to open a new bottle, and forgot to add bay leaves. No salt added beyond the overnight dry brine. I added about 2 cups of water half way through the cooking.
INSTRUCTIONS
Braising Work (Day Before)
Heavily salt the exterior of the short ribs. (optional) Let dry brine for at least 3 hours or overnight in the fridge.
On the day of braising, preheat the oven to 275 F. Prep the mirepoix by dicing the white onion, carrot, and celery. It should roughly be 2 parts onion, 1 part carrot, 1 part celery.
Set a dutch oven or braising pot over medium-high heat and add the oil. Once hot place the short ribs down and sear on all sides. Take your time to develop a nice crust on all sides. Once browned, set the ribs aside and turn the heat down to medium.
Add the diced onion, carrot, and celery along with a big pinch of salt and cook while stirring for about 10 to 15 minutes until the onion is nicely browned.
Add the tomato paste and cook just for about a minute until it turns a deep red. Pour in the wine and scrape the bottom of the pan to release any fond that has developed. Let cook for 2 minutes to slightly reduce the wine.
Return the browned ribs to the pot and add enough stock or water to the pot so it comes 3/4 of the way up the ribs. Bring the liquid to a simmer then partially cover the lid and slide in the preheated 275 F oven.
Let the ribs braise for roughly 4 hours which will allow enough time for the collagen to turn into gelatin making them fork tender. Once fork-tender, pull the pot out of the oven and let cool until the liquid reaches 140 F and the ribs are cool enough to handle.
If desired, you can remove the bone and clean up the ribs before storing it. Move the ribs to an airtight container and store in the fridge. Strain the cooking liquid into a container and set it in the fridge overnight so the fat congeals to the top.
Next:
Remove the fat from the cooled cooking liquid. Set a pan over medium-low heat and add the liquid to the pan, bring to a simmer and let slowly reduce while stirring for about 20 minutes. Be careful not to burn!
When the cooking liquid has reduced so it leaves a trail with a spatula, add in the short ribs and coat the exterior to bring them up to temperature. Turn the heat off and set a lid on top.