In 12-inch skillet over medium-high heat, in 2 tablespoons oil, cook half of eggplant slices until lightly browned and tender on both sides, turning once. Repeat with 2 tablespoons oil and eggplant.
Cut cheese into ½-inch-thick slices. In same skillet over medium heat, in remaining tablespoon oil, cook cheese slices until golden brown on both sides. Remove to plate.
To serve, place one eggplant slice on plate; top with a tablespoon marinara sauce, a basil leaf and a cooked cheese slice, cutting cheese slices to fit. Repeat two more times. Top with tablespoon marinara sauce. Garnish with basil slivers. Repeat with remaining eggplant and cheese slices. Serve immediately.