In a bowl or liquid measuring cup, stir together the broth, vinegar, tomato paste, and mushroom powder ‘til thoroughly combined.

Pat the short ribs dry with a paper towel, then season them all over with the salt and pepper.

Select the Sauté setting and heat the tallow or oil in the Instant Pot for 2 minutes. Using tongs, lower half of the ribs into the Instant Pot, searing them for 4 minutes per side (8 minutes total). Transfer to a dish and repeat with the rest of the ribs.

Add the onion and olives to the pot and sauté for 5 minutes, until the onion is softened and translucent. Pour in the liquid mixture, using a wooden spoon to nudge any browned bits from the bottom of the pot.

Add the short ribs back to the pot, turning them around with tongs to coat them in the cooking liquid. Work quickly so that not too much of the liquid evaporates. Arrange the short ribs in as even a layer as possible (you may need to stand them on their ends to fit).

Secure the lid on the Instant Pot and set the Pressure Release to Sealing. Cancel the cooking program, then select the Pressure Cook or Manual setting and set the cooking time for 35 minutes at high pressure. (It will take about 10 minutes for the pot to come to pressure before the cooking program begins.)

When the cooking program ends, let the pressure release naturally (this will take about 30 minutes). Open the pot and, using tongs, transfer the ribs to a serving dish and cover with a lid or aluminum foil so that they stay warm. Wearing heat-resistant mitts, lift out the inner pot, strain the cooking liquid into a fat separator, add the cooking liquid and solids back to the pot, and discard the fat or save it for another use. Return the pot to the housing.

Cancel the cooking program, then select the Sauté setting and reduce the sauce for about 15 minutes, until about 2 cups of the sauce remain. Cancel the cooking program to turn off the pot.

Spoon the sauce over the ribs and serve.