How to Make It
Preheat oven to 400°F. Combine breadcrumbs, 2 tablespoons oil, 1/2 teaspoon salt, and 1/4 teaspoon pepper in a medium bowl; toss to coat. Set aside. Cut kernels from corn cobs (You will have about 2 1/2 cups kernels). Set aside.
Toss together eggplant rounds, 1/4 cup oil, 1 teaspoon salt, and 1/2 teaspoon pepper in a medium bowl until well coated. Arrange eggplant in a single layer on a lightly greased, aluminum foil–lined baking sheet. Brush top of each eggplant round with about 3/4 teaspoon mayonnaise and sprinkle with about 2 1/2 tablespoons breadcrumb mixture. Bake in preheated oven until eggplant is tender and breadcrumbs are golden brown, 20 to 22 minutes.
Meanwhile, heat remaining 2 tablespoons oil in a large skillet over high. Add corn kernels, remaining 1 teaspoon salt, and remaining 1/2 teaspoon pepper. Partially cover skillet, leaving about a 2-inch gap (for steam to escape and to prevent corn from popping out of skillet). Cook, shaking skillet occasionally, until corn is well charred, about 8 minutes. Remove from heat, and let cool in skillet, partially covered, 1 minute. Transfer charred corn to a bowl.
Arrange 4 eggplant rounds on each of 4 serving plates. Top each of the 4 servings with about 1/3 cup corn, 1/4 cup crumbled feta, and 1 tablespoon mint. Drizzle with chile oil.