Remove the stems of the eggplants and cut each in half lengthwise. With a small pointed knife, make several shallow cuts in a checkerboard pattern on the cut surfaces of each eggplant. If using the larger American eggplant, cut it into four disks crosswise and make several shallow checkerboard cuts on both cut surfaces.

Heat 1 inch of vegetable oil in a skillet and cook the eggplant over medium heat until the cut surface is golden. Turn the eggplant over and cook it through, about 3 minutes over medium-low heat. Drain the eggplant on a paper towel.

Serve equal amounts of the eggplant on four serving plates, with the yuzu miso sauce spread over the surface and topped with the poppy seeds in the center.