Combine the pork, vegetable oil, coriander, garlic, orange zest, oregano sprigs, the intact half onion and a pinch salt in a large, wide pot. Add water to cover by 1/2 inch. Bring to a boil over medium-high heat, then reduce the heat to maintain a low simmer and cook, covered, stirring occasionally, until the pork is very tender, 2 to 2 1/2 hours. Increase the heat to medium-high. Uncover and boil until all of the water reduces, about 1 1/2 hours more. Continue to cook as the pork starts to fry in the fat, stirring the meat and scraping the bottom of the pot occasionally, until crispy in spots and well browned all over, about 15 minutes. Transfer the carnitas to a serving bowl, leaving the zest, oregano sprigs, onion and excess fat in the pot.
Serve the carnitas in doubled up corn tortillas with the cabbage, cilantro, radishes and chopped onion for topping.
Recipe courtesy of Rev Run's Sunday Suppers