Reduce the wine. Bring wine to a boil in a medium sauce pan over high heat. Reduce heat to medium and cook until wine is reduced by half, about 15 minutes. You want to end up with 1 cup of reduced wine—if you overdo the reduction, just add enough unreduced wine to bring it back to a cup. I learned this tip from Chef Daniel Boulud—he says it makes a sauce taste as if it has cooked for days. If you don't want to do this, just use 1 cup of unreduced wine when it's time to add it to the pot.
Season short ribs with salt and pepper. Heat 2 tablespoons of oil in the Instant Pot, set on Sauté. Working in batches so you don't crowd them, brown short ribs on 2 sides. Two or three minutes per side will do—you don't need to char them, just let them release that flavor into the pot. Set ribs aside.
Add onion and carrots to the pot, along with a little more oil, if needed. Season with salt and pepper, and cook, stirring frequently, for 2 to 3 minutes. Clear a space in the middle and add garlic and thyme. Cook until fragrant, stirring constantly, about 45 seconds. Add rosemary, beef stock and reduced wine to pot, and stir, scraping up any browned bits.
Return ribs to the pot. You can cram them in pretty tight, but you still may need to put a couple on top of the rest. That's okay. Seal the lid of the Instant Pot and set to cook on high pressure for 40 minutes. When the cycle is done and the Instant Pot shuts off, let it sit for 10 minutes, then using an oven mitt, carefully turn the steam release handle. When the float valve drops down, remove the lid.
Transfer the short ribs to a plate and tent with foil. Many of the bones will fall out—you can bid them farewell or salvage them to artfully reinsert them when you plate the ribs.
An impressive layer of fat will float up to the surface of the sauce. Get rid of as much as you easily can—I used a grease separator. Transfer sauce, carrots and onion to a sauté pan. Discard the rosemary stems (the needles will have cooked off them) and bring sauce to a boil.
Cook until sauce is reduced a bit, about 5 minutes. In a small bowl, stir corn starch into 1 tablespoon of cold tap water. Spoon a little sauce into the bowl to slightly warm it, then stir the corn starch mixture into the sauce. Cook for a minute or 2, stirring frequently, until sauce thickens. Add ribs to pan to warm them, cooking a minute or 2.
Divide warm mashed potatoes among 4 plates, mashing down to create a base for the ribs. Set ribs on potatoes and spoon sauce, along with carrots and onion, over everything. Serve.