Remove rib roast from refrigerator about 3 hours before starting recipe to allow it to come closer to room temperature.
Season rib roast by rubbing and coating all sides with salt and pepper.
Press Sauté on the Instant Pot and allow it to heat until it says "HOT". Add 2 tablespoons of butter and coat the bottom.
Once the butter has melted, place the roast into Instant Pot and brown all sides, 5 minutes per side (about 20 minutes). Remove the rib roast and set aside.
With the Sauté function still on, add the wine into Instant Pot and scrape the bottom. Allow the alcohol to cook off for about 3 minutes.
Add the beef stock and turn off Instant Pot. Place the trivet on the bottom over the liquid.
Place the rib roast on top of the trivet with the fat cap side up. Place the garlic head on top. Place the lid on top and set the valve to Sealing. Program the Instant Pot for manual high pressure cook for 12 minutes. It will take about 7 minutes to come to pressure first.
Once the time is up, allow it to sit for 35 minutes if your roast is closer to 5 pounds or 40 minutes if your roast is closer to 6 pounds.
Remove the lid and measure the internal temperature of the rib roast right in the middle of the thickest part. The temperature should be about 115 F. If the temperature is too low, replace lid and allow it to sit for 5 more minutes. Repeat until the temperature reaches 115 F.
Remove the rib roast and set aside. Pour off the liquid into a heat-safe container, squeeze the garlic into liquid, and reserve it to make the au jus.
Press Sauté on Instant Pot and allow it to heat until it says "HOT". Add the remaining butter and coat the bottom. Once butter has melted, place roast into Instant Pot and sear all sides again, about 5 minutes total. The internal temperature should now be approximately 125 F to 130 F for medium-rare.
Remove the roast to a cutting board. Turn off the Instant Pot and pour off the small amount of remaining liquid and discard.
Tent the roast loosely with tin foil and allow it to rest for 15 to 20 minutes.
While roast is resting, skim the fat off the top of the liquid reserved from Step 10, break up the garlic pieces with the back of the spoon, and then add it to Instant Pot and set to Keep Warm until ready to use.
Strain the liquid into a serving dish using a mesh sieve right before serving.
Slice roast into ½- to ¾-inch slices. Serve with au jus.