Turn Instant pot to Saute setting. Once hot, add one tablespoon of oil. Once hot, add onion and carrots and cook for a few minutes, stirring constantly. Remove veggies to a plate.
Pat the ribs dry with paper towels, season on all sides with salt and pepper and coat on all sides with flour. Add 2 more tablespoons of oil to the pot. Add ribs and brown on all sides, then remove to a plate.
Add the wine to deglaze the pan. Scrape the bottom of the pan to release any browned bits of flavor. Bring to a boil and cook 2 minutes.
Add beef broth, salt and freshly ground black pepper. Stir in tomato paste. Return ribs, and veggies to the pot and add sprigs of thyme and rosemary.
Secure instant pot lid. Cook on Manual/High Pressure for 45 minutes with a 15 minute natural release.
Remove instant pot lid, and carefully remove short ribs to a plate and cover to keep warm.
Turn pot to saute and add cornstarch slurry. Cook until sauce has thickened. Serve ribs over mashed potatoes with a spoonful of gravy from the pot.