1To make the sauce, in a saucepan over medium heat, combine the soy sauce, mirin, brown sugar, ginger, and garlic. Bring the mixture to a boil, then reduce the heat to low and simmer until the mixture becomes slightly syrupy, about 5 minutes. Let cool.
2Place the pork chops in a large zippered plastic bag. Pour half of the teriyaki sauce over the pork and refrigerate for 8 hours or overnight. Reserve the other half of the sauce.
3Prepare a charcoal grill for medium-high heat. Clean and oil the grill grate. While the grill is heating, remove the pork chops from the marinade and let come to room temperature.
4Arrange the pork chops on one side of the grill and the pineapple slices over the other side of the grill. Cover the grill and cook, turning the chops and pineapple occasionally, until the chops are nicely seared and cooked to medium (about 145–150°F) and the pineapple slices are nicely grill-marked. Transfer the chops and pineapple slices to a platter, tent with foil, and rest for 10 minutes.
5Garnish with sesame seeds. Serve with the rice, passing the reserved teriyaki sauce on the side.