1. In 6-quart pressure cooker, melt 1 tablespoon butter over medium-high. Place flour in a shallow dish. Season beef with salt and pepper, then coat in flour, shaking off excess. Add beef to pressure cooker and cook until browned on all sides, about 8 minutes. (Brown beef in batches, if necessary.) Transfer to a plate. Add onion, garlic, and thyme to pressure cooker and saute until soft, 4 minutes. Add red wine and 1/4 cup water and cook, stirring and scraping up browned bits with a wooden spoon, 1 minute. Return beef to pressure cooker.

2. Fill steamer basket insert with potatoes and carrots and place over meat. Secure lid and bring to high pressure over medium-high heat; reduce heat and cook until meat is tender, about 50 minutes (adjust heat to maintain pressure). Remove from heat, vent pressure, and remove lid.

3. Transfer vegetables to a bowl with remaining 2 tablespoons butter, and mash; season with salt and pepper. Serve short ribs with potato-carrot mash and drizzle with cooking liquid.