If you’ve brined your pork tenderloin: rinse it well and pat it dry before these steps.
Make the dry rub: Mix the smoked paprika, garlic powder, Italian seasoning, onion powder, Kosher salt, and cracked pepper in a small bowl, then set aside.
Start the sauce: In a medium-sized mixing bowl, whisk together the chicken broth, maple syrup, soy sauce, liquid smoke, and BBQ sauce; set aside.
Season and sear the pork: Heat oil in the Instant Pot on low on sauté mode. Rub the pork evenly with the dry rub, then cut the tenderloin in half so it fits in the pot. Using tongs, carefully place both pieces of pork tenderloin in the Instant Pot and cook each side for 1-2 minutes, or until the pork has browned on each side.
Add sauce and pressure cook: Pour the sweet and smoky sauce into the pot over the tenderloin. With a large spoon or spatula, try to scrape up any pan bits from cooking the pork. (Pan bits can trigger the burn notice, even though nothing is burning.) Secure the lid on the Instant Pot, lock it, and set the valve to “seal”. Pressure cook on high for 3 minutes.
Natural release and rest: When the Instant Pot beeps to indicate the pork is done, let the pressure release naturally. This should only take about 12 minutes. If it goes longer, do a quick release. Remove the lid and, using tongs, transfer the pork to a cutting board. Let it rest for at least 5 minutes before cutting into it.
Thicken the sauce: Set the Instant Pot to Sauté mode (medium) and let the sauce reach a simmer. While you wait, mix 2 tablespoons cornstarch with 1/4 cup cold water in a small bowl until the cornstarch fully dissolves to make a slurry. Once the sauce simmers, whisk in the slurry. Keep whisking until the sauce thickens to a gravy-like consistency.
Slice and serve: Cut the tenderloin into 1/2-inch-thick portions and transfer to a serving platter. Drizzle with the sauce and garnish with fresh chopped parsley.