Cut scallion greens into 1-inch lengths, reserving white parts for another use. Pat seafood dry and season with salt and pepper. Heat 3 tablespoons oil in a 12-inch nonstick skillet over moderately high heat until hot but not smoking, then stir-fry eggplant with salt and pepper until golden brown on both sides and cooked through (add 3 tablespoons more oil if eggplant is sticking to skillet). Transfer eggplant to a plate as cooked and keep warm, covered.
Add 2 tablespoons oil to skillet and sear shrimp and scallops in batches, without crowding, until just cooked through, about 4 minutes. Add more oil to skillet if necessary. Transfer to plate and keep warm, covered.
Add water, soy sauce, sugar, and chile paste to skillet and simmer, stirring, until reduced by half. Stir in lime juice. Serve seafood and eggplant with sauce, scallion greens, cilantro, and basil.
Cooks' note: Eggplant is a sponge for oil. Don't add more oil, even if skillet looks dry, unless eggplant sticks.