Sweat eggplants: Peel the eggplant skin in stripes (you don't have to peel all of the skin off). Cut each eggplant in half vertically. Make slits over the surface but don't cut through the skin. Sprinkle salt over the eggplant surfaces and let them sweat for at least 10 minutes.
Starch slurry: Meanwhile, mix together the corn starch and water to make a slurry. Set aside.
Miso glaze: Make the miso glaze by combining dashi, miso, sake, mirin, and maple syrup in a small saucepan over medium low heat. Stir continuously. When the miso mixture starts to simmer, add the corn starch slurry and continue to mix until the glaze has thickened. Turn off the heat and let sit while you prepare the eggplants.
Microwave eggplants: Wipe off the liquid that comes out on the surface of the eggplants. Spray/brush oil over the surface of the eggplants. Microwave 2½ minutes, flip, and microwave another 2½ minutes. The eggplants should be tender.
Brown eggplants: Heat a pan over medium heat. Brush oil over the cut sides of the eggplants. Place the eggplants cut side down on the frying pan and cook until browned. Brush remaining oil on the other side of the eggplants, flip, and brown.
Glaze: Transfer eggplants to a plate cut side up and pour the miso glaze on top.
Notes
*If using dashi powder, mix 1/2 tsp dashi with 1/2 cup water.