In a large mixing bowl, stir all of the sauce ingredients together until well blended; set aside.
Place the pork onto a cutting board and carefully cut the pork into three even pieces. Massage the dry rub over each piece.
Set the Instant Pot to Sauté mode. Drizzle the oil into the pot to warm it, then carefully place one of the pieces of pork into the pot. Sear it on all sides, about 2 minutes per side. Remove the pork and place it on a clean surface; repeat this with the other two pieces of pork. By searing the pork cuts, you'll get a nice rich crust which brings more flavor and crispy bits of pork similar to the "bark" you'd get from smoked pork.
Transfer 1 cup of the Korean-inspired sauce to the Instant Pot plus 1/2 cup of water, and return your pieces of pork to the pot. They'll be snug, but that's okay.
Secure the lid on your Instant Pot, set the valve to 'Sealing', and cook on HIGH manual pressure for one hour. When done, let the pressure naturally release for 15 minutes. Don't do a manual quick release, or the pork will seize up and lose tenderness. Once the 15 minutes are up, then it's safe to manually release the rest of the pressure.
While the pork cooks, make the slaw. Mix the lime juice, brown sugar, and salt together in a mixing bowl, then toss the cucumbers and slaw into the liquid and let them sit. This will give the veggies a nice quick pickle. Before topping the pork, you can toss some sesame seeds in with the veggies.
Carefully remove the pork cuts from the Instant Pot and place them onto a cutting board. Drain all but 1 cup of the liquid from the inside of the Instant Pot. Using two forks or meat claws, shred the pulled pork—the pork should be incredibly tender and shredding it should be effortless.
Transfer the pulled pork back into the Instant Pot and drizzle the rest of the Korean-inspired sauce over it; toss to coat. Garnish the pulled pork with sesame seeds and sliced scallions, and serve with fresh brioche buns or crisp bibb lettuce for lettuce wraps.