In a large bowl, whisk together the light brown sugar, garlic powder, onion powder, thyme, rosemary, kosher salt, and pepper.
Season all sides of the pork roast with the spice rub.
Turn the Instant Pot to SAUTE. Once heated, add 2 tablespoons of olive oil, then add the pork roast and sear on all sides, about 3 to 5 minutes. Once the pork is browned on all sides, remove it from the Instant Pot and transfer to a plate. Set aside.
Press CANCEL, then pour a little bit of chicken broth into the pot, about 2 Tablespoons full to start. Using a wooden spoon, deglaze the pot by scraping up any brown bits at the bottom of the pot. Add a little bit more chicken broth as needed to scrape up all of the browned bits. This helps you avoid a BURN notice during pressure cooking.
Press SAUTE on the Instant Pot and add the remaining 2 Tablespoons of olive oil. As it heats up add the garlic and onions and sauté for 1 to 2 minutes, just until they are soft and fragrant. Then press CANCEL.
Pour in the rest of the chicken broth and the red wine. Lower a trivet or Instant Pot sling into the pot and place the pork roast on top of it. Place the rosemary sprigs on top of the pork roast.
Close the lid, making sure the pressure release valve is in the SEAL mode. Select PRESSURE COOK (or MANUAL, depending on your pressure cooker), select HI for temperature, and set the time to 1 hour and 10 minutes (70 minutes). The Instant Pot will take anywhere from 6 to 15 minutes to come to pressure, then it will pressure cook for 1 hour and 10 minutes.
Once pressure cooking is complete, do a Quick Release: use tongs or a wooden spoon to carefully move the pressure release valve over to VENT position. Once all pressure has been released, the pressure release valve pin will go down. Once that pin is down, you can press CANCEL and very carefully open the lid.
Add the carrots and potatoes to the Instant Pot, positioning them around the pork roast and some on top.
Return the lid to the Instant Pot, and secure it, ensuring the pressure release valve is in the SEAL position.
Select PRESSURE COOK (or MANUAL), HI temperature, and a cook time of 4 minutes.
Once pressure cooking is complete, do a Quick Release. Once all pressure has been released, the pressure release valve pin will go down. Once that pin is down, you can press CANCEL and very carefully open the lid.
Carefully remove the pork and vegetables from the Instant Pot and transfer to a large plate or large bowl. Set aside.
Select SAUTE. Add the balsamic vinegar and cornstarch to the liquid remaining in the Instant Pot. Whisk together vigorously as the liquid comes to a low boil, whisking out any cornstarch clumps as you go. Continue to whisk and allow the liquid to thicken to a gravy, which takes anywhere from 2 to 5 minutes. Once the gravy is to your desired level of thickness, press CANCEL and transfer the gravy to a gravy boat.
Plate the pork roast with the vegetables, and serve with the gravy.
Notes
Pork: A pork roast that is 2-4 lbs is recommended. You may need to increase the pressure cook time if you have a 3 or 4 lb roast. Pork is done when a thermometer inserted into the center of the pot roast shows an internal temperature of 145°F.Storage: allow the pork roast and vegetables to cool completely, then place in airtight containers and refrigerate for up to 4 days or freeze for up to 1 month.