Preheat oven to 300 degrees F.
Pat short ribs dry with a paper towel and salt and pepper the ribs on top and bottom.
Heat 2 tablespoons olive oil in a large oven-safe pot (with a lid for later) over medium high heat. Once it is hot begin browning the meat, in batches if necessary, about 2 minutes per side. Make sure you get a nice brown crust on each side because this seals in the juices. If your oil starts disappearing you can add a little more. Finding the sweet spot with the heat for getting a nice sear and not cooking so hot that the oil starts burning is the key. Don’t rush this step.
When the meat has finished browning set it to the side, patting off any excess grease with a paper towel.
Add the onions to the pot and begin to cook over medium high heat. You should have enough grease in the pan from the short ribs but if you need to add a little olive oil you can. Cook for about 5 minutes and then add your carrots, celery, and garlic. Continue to cook for another 5-7 minutes until softened.
Pour the wine into the pot and cook over medium high, bringing it to a boil and then cooking for 5 minutes. Use your spoon to scrape up any browned bits off of the bottom.
Place the browned short ribs into the pot arranging them so that as many of them are in the vegetables and wine as possible.
Wrap your rosemary and thyme in cheesecloth and nestle it between the meat. If you don’t have cheesecloth you can just nestle the herbs in amongst the meat but the cheesecloth makes it easier to remove everything at the end.
Pour in enough beef broth to bring the liquid up to almost cover the short ribs. Some can be partially above the liquid.
Place a tight lid on the pot and put it in the oven to cook for 3.5 - 4 hours. You’ll know they are done when they smell amazing and you can pull the meat apart easily with a fork.
Remove the meat from the juices and then let the juices cool enough to handle. Place a fine mesh strainer, or a regular strainer with cheesecloth in it over a large bowl and pour your juices through it.
Herbs and veggies will be removed. You can serve the vegetables if you like but I do not.
Skim excess fat off the top of the juices before serving. See note below about making ahead of time.
Serve beef over mashed potatoes or creamy polenta with a few spoonfuls of the juices over top.