Mix all of the spices, with only 1 teaspoon of salt, in a small bowl. Rub the mixture into all sides of each piece of pork, using your fingertips to rub it in until the outside turns a red hue from the paprika and chili powder.
2 teaspoons dried oregano, 3 teaspoons cumin, 1 teaspoon EACH: smoked paprika, garlic powder, onion powder, and chili powder, 1/2 teaspoon black pepper, 2 teaspoons kosher salt
Drizzle the olive oil into the bottom of the Instant Pot and turn it to the saute function until it's hot and shimmering. Working in batches, sear 4-5 pieces of pork shoulder for 2-3 minutes on each side, until crispy and brown. Transfer the seared pork to a cutting board.
2 tablespoons olive or avocado oil, 3 lb pork shoulder (pork butt)
Pour in a bit more oil in the bottom of the pot and add the onion and cook to soften for 2-3 minutes, until translucent. Add the garlic and cook for another 1-2 minutes, until fragrant.
6 cloves garlic, 1 medium white onion
Add the pork shoulder back to the Instant Pot. Pour in the lime juice, orange juice, broth, remaining teaspoon of salt, and bay leaves. Stir it together, scraping any brown bits from the bottom of the pan. Cancel the saute setting close the lid and turn the pressure valve to the sealing position.
2 bay leaves, 1/3 cup fresh orange juice, 1/3 cup fresh lime juice, 1 cup chicken broth
Cook on high pressure for 55 minutes. It will take about 10 minutes for Instant Pot to come to pressure before it counts down. When the timer goes off, naturally release the Instant Pot (do nothing) for 10 minutes then turn the pressure release valve to quick release (release the remaining pressure).
Preheat the oven to broil. Use a slotted spoon to remove the cooked pork pieces from the Instant Pot onto a sheet pan. Shred the pork with two forks. It should fall apart easily.
Spread it out evenly onto the sheet pan and broil it in the oven for 3-5 minutes, turning the pan once or twice to crisp it evenly. Serve warm in tortillas, a burrito, or in a burrito bowl.
For serving: