Whisk eggs with pinch of salt until blended. Heat 1 tablespoon oil in wok or heavy large skillet; add eggs and using spatula, lift eggs as they cook, letting uncooked part run underneath until set. Transfer to cutting board. Cut eggs into shreds.
Heat 2 tablespoons oil in same wok over medium-high heat. Add ham and vegetables and stir-fry 1 minute. Add shredded eggs, rice and 1 tablespoon soy sauce and stir-fry until heated through. Season with pepper. Serve, passing soy sauce separately.