2largecarrots, cut into 1/2 inch dice (about 1 cup)
2ribscelery, cut into 1/2 inch dice (about 1/2 cup)
1mediumonion, chopped or halved and sliced
5garlic cloves, peeled and sliced for Dutch oven method, peeled and lightly crushed (whole) for Instant Pot
2cupsbeef broth, plus additional, if needed
1tablespoon Worcestershire sauce
1largedried bay leaf
kosher salt and freshly-ground black pepper
chopped fresh parsley, for garnish
mashed potatoes, colcannon, polenta, or egg noodles, for serving
Preheat oven to 300 degrees F, with the rack in the lower third of the oven. Dry the short ribs with paper towels and season well on all sides with salt and pepper. Dredge in flour, shaking off excess.
Heat the oil in a large (6-7 quart) Dutch oven over medium-high heat until shimmering. (If the short ribs don't fit in a single layer, work in batches.) Brown short ribs on all sides, turning every 2-3 minutes as needed. Transfer to a plate and set aside.
Pour off all but 2 tablespoons oil from the pot. Add carrots and sauté 3 minutes. Add celery and onion with a few pinches of salt and pepper, and sauté until onions begin to brown. Stir in tomato paste and garlic, and cook for an additional 1-2 minutes.
Add stout, scraping the brown bits off of the bottom of the pot. Stir in Worcestershire sauce. Return browned short ribs to the pan (plus any accumulated juices).
Tie the rosemary and thyme together with kitchen twine for easy removal. Add the herbs to the Dutch oven with the bay leaf. Stir in beef broth. The liquid should come about 3/4 of the way to the top of the short ribs.
Bring to a simmer, cover the Dutch oven, and bake for 3 hours, until the short ribs are fork tender. Turn the short ribs after about an hour and a half. If a lot of the liquid has evaporated, add some extra broth.
Prep and sear the short ribs, saute the vegetables, and deglaze the pan with stout, as in the Dutch oven method. You can use the Instant Pot insert with the SAUTE setting on HIGH to do this in batches, but I prefer to use a pan on the stove for better results. (Important: Read more about why in theInstant Pot Tips section of the article above.)
Add the contents of the deglazed pan, with the aromatics and stout, to the Instant Pot insert and stir in the Worcestershire Sauce. Add the seared short ribs, bay leaf, and tied fresh herbs. Pour in the beef broth.
Place the lid on the Instant Pot, set the valve to "sealing," and cook on HIGH pressure for 45 minutes. Let the pressure release naturally for 15 minutes, and then manually release the remaining pressure.
For Both Cooking Methods
Remove short ribs from the pot with a slotted spoon and cover with foil. Strain the braising liquid, gently pressing on the vegetable solids with a spoon or spatula to remove as much liquid as you can. Discard the solids.
Let the braising liquid stand for about 5 minutes. Use a gravy separator or a spoon to skim the top of the liquid and remove excess fat.
Whisk Dijon mustard into the defatted liquid and simmer until it's thick enough to coat the back of a spoon. You should have 2 to 2-1/2 cups of gravy.*
Season the gravy to taste with salt and pepper. Spoon over short ribs and serve with mashed potatoes, colcannon, polenta, or egg noodles. Garnish with chopped parsley.
*For a thicker gravy, make a slurry by dissolving 2 tablespoons of cornstarch in 2 tablespoons of cool water. Whisk the slurry into the sauce a teaspoonful at a time, simmering and adding enough of the slurry to reach your desired thickness (you might not need all of it). Cooking times listed in the card are for the Dutch oven method. The Instant Pot method requires 50 minutes of prep (including searing the meat, sautéing the aromatics, and making the gravy), and 85 minutes of cooking time (including pressure cooking, pressurization time, and pressure release). 2 hours and 15 minutes total.For make-ahead instructions, see the FAQ's in the article above.