Preheat oven to 425°. Brush both sides of eggplant slices with oil and place on a parchment paper-lined baking sheet. Roast eggplant, flipping once, until very tender, about 20 minutes. Remove from oven. Arrange a rack in upper third of oven and heat to broil. Meanwhile, whisk white miso and next 5 ingredients with 1 Tbsp. water in a small bowl. Stir in 1 1/2 tsp. sesame seeds and 2 Tbsp. scallions. Smear top of eggplant slices with miso sauce. Broil until golden and charred in places, 4–5 minutes. Remove from oven and sprinkle with remaining 1 1/2 tsp. sesame seeds and 1 Tbsp. scallions.