Adjust oven racks to the upper-middle and lower-middle positions and heat to 450 degrees. Line two rimmed baking sheets with aluminum foil and spray with oil. Toss the eggplant with vegetable oil and the first portion of soy sauce, then spread evenly between the prepared sheets. Roast until the eggplant is tender and deeply browned, about 25 to 30 minutes, switching and stirring the sheets halfway through so they cook evenly.

Whisk the sugar, oyster sauce, sesame oil, sake, chili-garlic sauce, and remaining soy sauce in a small saucepan over medium heat. Once the sugar has dissolved and the sauce is uniform, about 1 minute, cover and set aside to keep warm.

Cook the noodles in a large pot of boiling water until tender. Reserve some of the cooking water before draining the noodles and returning them to the pot. Add the glaze and roasted eggplant and toss to combine, adding the reserved water as needed to create a smooth sauce that coats the noodles. Serve hot, topped with cilantro and sesame seeds.