Adjust an oven rack to the middle position and heat the oven to 425°F. On a rimmed baking sheet, toss the eggplant with the oil and 2 tablespoons of the soy sauce until evenly coated. Spread the eggplant into a single layer so it roasts rather than steams.

Roast until the eggplant is tender and well-browned, about 25 to 30 minutes, stirring and rotating the pan halfway through.

Whisk the remaining soy sauce, sugar, vegetarian oyster sauce, sesame oil, sake, and chili-garlic sauce in a large bowl. Continue whisking until the sugar has completely dissolved.

Bring a large pot of water to a boil. Add the soba noodles and cook until tender but still firm to the bite. Drain the noodles and immediately rinse them under cold running water to stop the cooking and remove excess starch.

Add the rinsed noodles and the roasted eggplant to the bowl with the sauce. Toss gently with tongs or large spoons until the noodles are well-coated and the eggplant is evenly distributed.

Serve topped with the cilantro and sesame seeds while the noodles are still warm.