For the beet slaw, in a large bowl, whisk the lime juice and zest, honey, salt, and olive oil. Add the beets, cabbage, carrot, apple, and cilantro, and toss well to coat them all in the lime sauce. Cover and refrigerate until you’re ready to eat, stirring the mixture every once in a while.

In a medium bowl, whisk the lime juice and zest, garlic, honey, fish sauce, oil, salt, and pepper. Pour the marinade into a gallon-size resealable plastic bag, add the pork chops, press as much air from the bag as possible, and seal it. Turn the bag a few times to coat the pork in marinade and refrigerate for at least 30 minutes or up to 1 day.

Preheat your gas grill with all burners on high and close the lid. When the grill is hot (after about 15 minutes), turn the 2 burners closest to the front to low, keeping the back burner on high. Remove the pork chops from the bag, discard the remaining marinade, and arrange on the grates over the low heat burners. Cover and cook until the undersides of the chops are just beginning to develop light grill marks, 6 to 9 minutes. Flip them, cover, and continue to cook until the the pork is firm to touch, 6 to 9 minutes longer. To get a nice char on them, move the chops to the part of the grill over high flames and cook uncovered until each side has solid grill marks, 5 to 6 minutes, flipping halfway. The pork chops should be completely firm to the touch and register 145 degrees F on an instant-read thermometer. Transfer to a plate, tent with foil, and let rest for 5 minutes. Serve with beet slaw.