Heat the oven to 425°F and grease a 9-by-13-inch baking dish.
Toss the eggplant with 1/2 teaspoon salt, let it stand for 15 minutes and blot it dry with a clean towel.
Toss the eggplant with 2 tablespoons olive oil and roast it on a sheet pan for 20 minutes, turning once, until browned and tender.
Combine the roasted eggplant, farro, marinara, oregano, pepper, remaining salt, 1 1/2 cups mozzarella and 1/4 cup Parmesan in the baking dish.
Mix the panko with the remaining olive oil, mozzarella and Parmesan and scatter it over the top.
Bake for 20 to 25 minutes, until the sauce bubbles and the crumbs are crisp.
Rest for 10 minutes before cutting.