Preheat a grill to medium high. Combine 1 cup warm water, 2 tablespoons salt, 1 tablespoon brown sugar and half of the ginger in a large bowl; stir until dissolved. Add the pork chops; cover with cold water. Let sit 10 minutes. Drain and pat dry; season with salt.
Meanwhile, heat 2 tablespoons olive oil in a small skillet over medium heat. Add the remaining ginger and the red pepper flakes and cook until the ginger sizzles, 2 minutes. Add the vinegar and the remaining 3 tablespoons brown sugar. Cook, stirring occasionally, until the glaze thickens, 3 to 5 minutes. Transfer 2 tablespoons to a small bowl for basting; set aside the rest for serving.
Brush the grill grates with olive oil. Toss the eggplant, zucchini, scallions and tomatoes with the remaining 2 tablespoons olive oil in a large bowl; season with salt. Grill the vegetables until tender, 3 to 5 minutes per side; transfer the scallions to a cutting board and transfer the rest of the vegetables to a large bowl. Grill the pork chops until marked and cooked through, 4 to 6 minutes per side, basting with the reserved glaze during the last few minutes.
Chop the scallions; add to the vegetables along with the basil. Top the pork chops with the remaining glaze. Serve with the vegetables.
Shishitos, small Japanese peppers, are usually mild, but beware: One in every dozen or so is super spicy!