Set the oven racks to the upper-middle and lower-middle positions and heat the oven to 450°F. Line two rimmed baking sheets with aluminum foil and coat with vegetable oil spray. Toss the eggplant with vegetable oil and soy sauce in a large bowl, then spread evenly across the prepared baking sheets. Roast for 25 to 30 minutes, stirring the eggplant and switching the sheets' positions halfway through, until the cubes are tender and deeply browned.

Combine the sugar, oyster sauce, sesame oil, sake, chili-garlic sauce, and the remaining portion of soy sauce in a small saucepan over medium heat. Whisk often until the sugar has completely dissolved, about 1 minute, then cover the pan and set aside to keep warm.

Bring 4 quarts of water to a boil in a large pot. Add the noodles and cook, stirring frequently to prevent sticking, until tender. Reserve a half-cup of the cooking water, then drain the noodles and return them to the pot.

Add the sauce and roasted eggplant to the noodles and toss to coat. Use the reserved cooking water a splash at a time to loosen the sauce until it reaches a silky consistency. Serve immediately, topped with cilantro and sesame seeds.