For the Pork: Working 1 piece at a time, sandwich pork between layers of plastic wrap and pound with a meat pounder or heavy skillet until about 1/4 inch thick. Season generously with salt and pepper and set aside.
For the Miso Slaw: Combine cabbage, vinegar, and white miso in a medium bowl and toss. Season to taste with salt. Set aside.
For the Chutney: In a large bowl, drizzle plums, scallions, and jalapeño with oil and toss to coat. Season with salt. Light one chimney full of charcoal. When all the charcoal is lit and covered with gray ash, pour out and arrange the coals evenly over the charcoal grate. Set cooking grate in place, cover grill and allow to preheat for 5 minutes. Alternatively, set the burners on a gas grill to the highest heat setting, cover, and preheat for 10 minutes. Clean and oil the grilling grate.
Place plums, scallions, and jalapeños directly on the hot side of the grill and cook, turning, until plums, scallions, and jalapeño are charred and softened, 4 to 7 minutes, removing each to a platter or cutting board as they're done.
Add grilled plums to a large mixing bowl. Stem and seed jalapeño, then finely dice and add to plums. Chop up scallions and add to plums. Stir in mustard, mint leaves, and honey, using the back of a wooden spoon to mash plum. Season with salt and pepper, then stir in enough sugar to make the chutney fairly sweet (about 2 tablespoons, depending on how sweet the plums were). Set aside.
Grill pork, turning, until just cooked through, 2 to 3 minutes per side. Toast bread on grill.
To build sandwiches, pile miso slaw on each bottom bun, then top each with 1 piece of grilled pork. Spoon some plum chutney on top, then top with remaining grilled pork. Spread plum chutney on top buns and close sandwiches. Serve.