Position a rack in the lower third of the oven and heat the oven to 350°F.
Heat a 6- to 8-inch skillet over medium heat. Add the cumin and coriander seeds and cook until fragrant, stirring frequently, about 30 seconds. Transfer to a mortar or spice mill and grind coarsely.
Pat the lamb chops dry. Brush on both sides with 2 tsp. of the olive oil, then sprinkle with 2 tsp. of the ground seeds, 1/2 tsp. of the paprika, and 1/2 tsp. cayenne. Season with salt and pepper. Set aside.
Put the eggplant in a large bowl. Toss with 5 Tbs. of the oil. Transfer the eggplant to a heavy-duty rimmed baking sheet and sprinkle with salt and pepper. Bake, turning once halfway through, until the eggplant is almost tender and starting to brown on the bottom, about 25 minutes. Set aside.
Heat the remaining 1 Tbs. oil in a 12-inch nonstick skillet over medium heat. Add the onion and cook, stirring, until tender, about 6 minutes. Stir in the remaining ground spices, 1/2 tsp. paprika, and 1/8 tsp. cayenne. Add the tomatoes, chickpeas, and eggplant. Stir to combine. Cover and simmer until the eggplant is very tender and the flavors meld, about 10 minutes.
Meanwhile, heat another 12-inch skillet over high heat until very hot. Add half of the lamb chops in a single layer and cook until brown, about 2 minutes on each side. Reduce the heat to medium and cook about 2 minutes longer for medium rare. Transfer the lamb to a warm platter and cover to keep warm. Repeat with the second batch of lamb chops.
Add the shallots to the skillet and cook, stirring, until starting to soften, about 2 minutes. Add the wine and boil until syrupy, scraping up any browned bits, about 3 minutes. Add the wine mixture to the eggplant mixture and simmer to blend, about 1 minute. Season to taste with salt and pepper. Divide the lamb among 4 warmed plates. Spoon the eggplant mixture alongside, sprinkling it with a pinch of garam masala, and serve immediately.