In a saucepan, bring enough water to boil to cook the noodles.
Slice the eggplant into half inch slices, if it is Japanese eggplant, just slice it in half lengthwise. Grill the sliced eggplant on a griddle, gas grill, or skillet until lit is browned on both sides and soft all the way through. Set aside to cool for a few minutes.
Then, make your dressing by mixing all the remaining ingredients except for the cilantro, basil, and sesame seeds.
When the eggplant is cool enough to handle, but still warm, cut it into bite sized cubes and put it into the dressing, mix together, and let sit for at least 15 minutes to marinate and blend flavors.
When the water is boiling, cook the noodles per manufacturer's instructions. Soba noodles should not contain any egg and the flour is more delicate so be careful to stir constantly, make sure water is boiling rigorously, and when you strain the noodles cool down immediately. They should come out nice and bouncy to the touch.
Mix the cooled noodles with the marinated eggplant. Add basil, cilantro, and mix together. Serve at room temperature, or slightly warm if the eggplant is still warm.
Sprinkle some sesame seeds on top for garnish. Sometimes I like to add some chopped cashews or sliced almonds to the garnish as well.