Thinly slice half the shallot. Finely chop remaining shallot. Combine the mince, breadcrumbs, egg and finely chopped shallot in a bowl. Shape tablespoons of the mixture into 20 meatballs.
Cook the noodles in a saucepan of boiling, salted water, following packet directions, until tender. Rinse under cold water. Drain. Reserve 1/2 cup of the cooking liquid.
Meanwhile, heat a wok over medium-high heat. Add half the oil. Cook the meatballs, in batches, for 5 minutes or until browned. Transfer to a plate. Heat the remaining oil in wok over high heat. Add the carrot, garlic and ginger. Stir-fry for 2 minutes or until carrot is just tender. Add the sauce, reserved cooking liquid and meatballs. Stir-fry for 2-3 minutes or until meatballs are cooked through.
Add the spinach, thinly sliced shallot and noodles. Stir-fry, tossing gently, for 2 minute or until heated though. Serve sprinkled with sesame seeds and with lime wedges.