For the carnitas: Cut the pork into 2-inch cubes and set aside. Add the tamarind paste, brown sugar and chipotles to a blender and puree until smooth. Rub the pork cubes with the marinade, then place in a pressure cooker along with the orange juice, tamarind soda and lard. Lock the pressure cooker according to the manufacturer's instructions and set to pressure cook on high for 1 hour. Follow the manufacturer's instructions for releasing the pressure, then let sit for 15 minutes. Remove the pork and let cool slightly, then shred with two forks.
For the black beans: Fry the black beans in a saucepan with the lard, then transfer to a blender and pulse until coarsely blended.
To serve: Spread a spoonful of mayonnaise on each roll, then add some refried beans on the bottom half of each. Top with the shredded carnitas, red onion, avocado, cilantro leaves and the top half of the roll.
Heat a cast-iron skillet over medium-high heat. Add a thin layer of vegetable oil. Place the sandwiches in the skillet and use another cast-iron skillet to weigh down the sandwiches until crispy on the first side, about 2 minutes. Flip and repeat, about 2 minutes more.