Gather the ingredients.
Sprinkle the short ribs with salt and pepper.
In the pressure cooker or in a separate skillet or saute pan over medium-high heat, sear the beef ribs in the olive oil on all sides. Remove and set aside.
Add the onions and mushrooms to the pan and cook until the onions are lightly browned and softened. Add the garlic and cook for 1 minute longer.
Combine the onion mixture and ribs in the pressure cooker. Top with the potatoes and sprinkle lightly with salt and pepper.
Combine the beef stock and wine; pour over all.
Bring the pressure up to high and cook for 50 minutes. Unplug and let the pressure come down naturally before removing the cover, about 15 to 20 minutes.
Transfer the ribs and vegetables to a platter and keep warm.
Put the liquids in a gravy separator and discard the fat. Serve with the short ribs and potatoes or thicken the sauce.
If a thicker sauce is desired, bring the liquids to a simmer in a saucepan or in the cooker.
Combine 2 tablespoons of flour with 3 to 4 tablespoons of cold water and mix until smooth. Add to the simmering broth. Cook, stirring, until thickened. Serve the sauce with the short ribs.
Follow the first 3 steps and arrange the ribs, onion mixture, and potatoes in a heavy Dutch oven.
Cover and bring to a boil. Reduce heat to maintain a simmer; cook for about 2 1/2 to 3 1/2 hours, or until the short ribs are very tender.
Continue with sauce, if desired.