Season the lamb with kosher salt and let sit at room temperature for 30 minutes.
Meanwhile, prepare a grill for indirect cooking by either carefully pushing the hot coals to one side or preheating two burners on a gas grill to high. Brush the grate with oil.
Grill the lamb chops over high heat, turning once, until charred on both sides, about 8 minutes. Grill the lamb with the fat cap down until crispy, 1 to 2 minutes. Move the lamb chops over to the cool side of the grill, cover, and cook bone side down until medium rare and a meat thermometer inserted in the thickest part registers 120°F, about 5 minutes. Transfer to a cutting board. Using a mandoline, thinly shave the raw garlic over the lamb chops. Alternatively, thinly slice the garlic with a very sharp knife and scatter it over the lamb. Let rest for 10 minutes.
Meanwhile, grill the scallions and eggplant over high heat, turning once, until tender and lightly charred, about 5 minutes for the scallions and 10 minutes for the eggplant.
Arrange the scallions and eggplant on plates and top each plate with 2 lamb chops and the shaved garlic. Drizzle with a little pomegranate molasses and olive oil and sprinkle with flaky sea salt before serving.