Mash the flour, salt, queso fresco, chives, cilantro, and butter together to form small crumbles. Add 2 tablespoons sour cream and stir to combine. Add the water and stir to form a dough. Form the dough into 2-inch disks.
Heat 2 tablespoons of the oil in a skillet until hot. Lightly fry the dough, flipping halfway as each side browns (about 3 minutes). Set aside.
In a large heavy pan, heat the remaining oil. Sprinkle 1 tablespoon salt and pepper all over the pork. Sear the pork on all sides, remove and set aside.
Add the onion, garlic, 2 teaspoons salt, ¼ teaspoon black pepper, cumin, oregano, and red pepper flakes. Cook until the onions are opaque. Add the orange juice and beer. Place the pork into the liquid mixture, cover, and bake at 350 degrees for 2 ½-3 hours or until the pork is cooked through and tender.
Carefully remove the pork from the liquid and shred with two forks. Place the shredded pork back into the liquid.
When ready to serve, place heaping mounds of the pork onto the cooked disks. Top with your favorite toppers such as a dollop of sour cream, queso fresco, sliced radish, pickled onions, and chopped cilantro.