Liberally salt the ribs on all sides.
Turn the Instant Pot to Saute on High.
Heat 2 tablespoons olive oil and then add the ribs in a single layer without overlapping (you'll probably need to do this in a couple batches).
Sear the ribs for 3 to 4 minutes on each side.
Transfer to a plate and set aside.
If pot is dry, add a little more oil.
Add the carrots, onion, and garlic.
Add 1/2 teaspoon salt and stir until vegetables soften, about 3 minutes.
Stir in the tomato paste and cook for 2 minutes.
Add the wine and stir, scraping the bottom to set loose any caramelized bits.
Bring the liquid to a boil and cook until reduced by about a third, about 4 to 5 minutes.
Add the stock, thyme, and bay leaf. Then nestle the ribs into liquid. They won't be completely submerged.
Lock the lid into place, turn the valve to Sealing. Press Cancel and then press "Meat" or "Meat/Stew" and set on High. and set the timer to 40 minutes.
After cooking, naturally release for 20 minutes, then quick release for any remaining pressure.
Unlock and remove the lid.
Carefully transfer the ribs to a platter. They will be very tender, so be gentle!
Tent the ribs loosely with foil while you finish the sauce.
Strain the sauce into a large pot through a coarse strainer and then pour into a fat separator (or use a spoon to remove the fat from the surface of the sauce).
Place the cooked vegetables on a serving dish and tent with foil.
Pour the sauce back into the pot
Select Saute and adjust the heat to Normal.
Add the brown sugar and then bring the sauce to a simmer, stirring frequently until the sauce is the consistency of gravy, about 10 minutes.
Taste and add more salt, if necessary.
Pour some sauce over the cooked ribs and pass the rest at the table.
Serves with vegetables. Enjoy!