Pat 3 lb. boneless pork shoulder (Boston butt), cut into 4 large pieces, fat cap trimmed, dry; season well on all sides with kosher salt. Heat 2 Tbsp. vegetable oil in a large heavy pot over medium-high. Working in 2 batches if needed, cook pork, turning occasionally, until browned all over, 8–10 minutes per batch (keep an eye on the second batch; it will brown faster). Transfer pork to a plate if working in batches.
Meanwhile, peel 1 medium orange into big strips, then cut both oranges in half and squeeze juice into a fine-mesh sieve set over a measuring glass or small bowl to catch seeds; discard seeds (you should have ½–⅔ cup).
Nestle all pork pieces back into pot if needed and add orange peel, orange juice, 5 garlic cloves, smashed, one 3″ piece ginger, finely chopped, ⅓ cup soy sauce, ¼ cup mirin, 2 Tbsp. light or dark brown sugar, ¼ tsp. crushed red pepper flakes, and 2 cups water. Bring to a boil. Cover pot, reduce heat, and simmer 2 hours.
Remove lid from pot and simmer rapidly until pork shreds easily when pressed and sauce is thick enough to coat pork, about 1 hour.
Meanwhile, heat remaining ⅓ cup vegetable oil in a small saucepan over medium-high. Cook 3 large shallots, thinly sliced, stirring occasionally, until golden brown and crisp, 6–8 minutes. Using a slotted spoon, transfer shallots to paper towels to drain and immediately season with salt (save shallot oil for another use—like tossing vegetables in it before roasting or making a salad dressing).
Using a fork, break apart pork in pot just slightly. Spoon some steamed jasmine rice onto plates or into shallow bowls. Divide pork over and top with some sauce from pot. Scatter crispy shallots and some cilantro leaves with tender stems and mint leaves on top.