Freeze lamb, wrapped in plastic wrap, until firm, 30 minutes, to facilitate slicing. Trim lamb well and cut into 1/8-inch-thick slices. Halve lamb slices crosswise. In a large bowl toss lamb with cornstarch until coated well and season with salt and pepper.
In a bowl stir together sauce ingredients until combined well.
Cut eggplant into 1-inch cubes. Diagonally cut celery into 1/4-inch-thick slices and mince garlic. Discard stems from shiitakes and halve caps (quarter if large). Halve white mushrooms lengthwise. Discard tough stems from watercress.
Heat a wok or large heavy skillet over high heat until a bead of water dropped on cooking surface evaporates immediately. Add 2 tablespoons oil, swirling wok or skillet to coat evenly, and heat until hot but not smoking. Add eggplant and stir-fry until golden and tender, about 4 minutes. Add celery and stir-fry until crisp-tender, about 2 minutes. Add garlic and mushrooms and stir-fry until mushrooms are tender, about 2 minutes. Transfer mixture to a large bowl.
Add 1 tablespoon oil to wok or skillet and heat until just smoking. Stir-fry half of lamb, separating slices, until browned and transfer to bowl. Add remaining tablespoon oil and stir-fry remaining lamb in same manner, transferring to bowl.
Add sauce to wok or skillet and bring to a boil, stirring. Return lamb-vegetable mixture to wok or skillet and stir-fry until combined and heated through. Stir in watercress and season stir-fry with salt and pepper.
