Add 3 tablespoons of oil to the skillet and heat until smoking. Add half of the squid and stir-fry over high heat until curled and lightly browned, about 4 minutes. Pour the squid and any accumulated liquid into a bowl. Add 3 more tablespoons of oil to the skillet; when it shimmers, add the remaining squid and stir-fry. Return all of the squid and any accumulated liquid to the skillet and cook over high heat until the liquid is evaporated, about 2 minutes. Add the scallions, season with salt and cayenne and cook until the scallions are tender, about 1 minute. Transfer the squid and eggplant to plates. Sprinkle with the cashews and serve with lemon wedges.