Heat the oven to 450°F. Put the chicken in a roasting pan, breast side up. In a small bowl, mix together the soy sauce, molasses, and sesame oil.
Line a baking sheet with foil or parchment. Lightly brush the eggplant slices with peanut or vegetable oil and put them on the baking sheet. Put the eggplant and the chicken in the oven. Bake the eggplant, turning once, until it’s lightly browned and tender when poked with a knife, about 10 minutes. Set aside to cool. (Cut the slices in half if large.) Continue to roast the chicken for another 5 minutes. (for 15 minutes total) at 450°F, and then reduce the heat to 375°F. Brush the chicken with the soy sauce mixture and continue to roast, basting frequently, until the skin is golden and crispy, the internal temperature of the thigh is 170°F, or the juices run clear when the thigh is pricked with a fork, another 55 to 65 minutes. Remove from the oven and let cool.
Meanwhile, make the dressing. In a blender or food processor, combine the ginger, garlic, jalapeño, rice vinegar, and soy sauce; process until smooth. With the motor running, add both the oils in a steady stream.
When the chicken is cool enough to handle, remove the meat from the bones, discarding the bones and skin (or eat the skin as a treat). Pull the meat into 2-inch strips, put it in a large bowl, and add the eggplant, chopped cilantro, and scallions. Add the dressing and toss gently. Season with salt and pepper. Garnish with the sesame seeds and whole cilantro leaves and serve immediately.