Mix all of the spices 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 kosher salt divided, 2 teaspoons dried oregano, 1 teaspoon EACH: smoked paprika, garlic powder, onion powder, and chili powder, ½ teaspoon black pepper, 3 teaspoons cumin
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 oil or avocado oil, 3 lb boneless pork shoulder (aka 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.
1 medium white onion cut into large chunks, 6 cloves garlic roughly chopped
Pour in the lime juice, orange juice, broth, and bay leaves. Stir it togetheere, scraping any brown bits from the bottom of the pan. Cancel the saute setting and close the lid and turn the pressure valve to the sealing position.
2 bay leaves, ⅓ cup fresh orange juice, ⅓ 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.
When you're ready to serve, warm the burrito shells by heating over an open gas stove flame for 30 seconds on each side. You can also put them in the microwave for 30 seconds or use a large cast-iron skillet to heat on both sides for 20-30 seconds each.
Place about 1/4 cup of rice in the middle of the tortilla then top with black beans and crispy carnitas. Finish with your favorite toppings.
To roll the burrito, fold half of the burrito over the toppings and tuck it under, securing the toppings against the shell. Fold in both sides then finish rolling into a burrito. Serve whole or slice in half.