Preheat the oven to 400F.
Wrap the tofu with 2 sheets of paper towel and press the tofu between two plates for 30 minutes.
Once the tofu is dehydrated, cut it into small bite size (any shape is ok), and the thickness should be about 3/4 inch.
Cut the eggplant in half lengthwise and score it in a crisscross pattern. This will help the eggplant absorb more flavors. Immediately soak in water to prevent the eggplants from changing colors, and to remove the bitter taste. Drain and dry with paper towel.
Place the tofu and eggplants (skin side down) on a rimmed baking sheet lined with parchment paper. With a brush, apply vegetable oil on top and bottom of tofu and eggplants.
Bake for 30 minutes, or until the eggplant is tender.
Transfer the baking sheet to the working surface. Adjust a rack 6-inches from the heat element and preheat broiler for 3 minutes.
Meanwhile carefully spoon some of the miso glaze onto your tofu and eggplants and spread evenly. Broil for 3-4 minutes, or until the top has nice char and caramelization.
Transfer to a serving platter, sprinkle with sesame seeds, and serve immediately.