To prepare the noodles, cook according to package directions, omitting salt and fat. Rinse with cold water, and drain well. Combine noodles, 1 1/2 teaspoons sesame oil, and 1 teaspoon vegetable oil in a large bowl; toss well to coat. Divide noodle mixture evenly into 6 (1-inch-thick) nests on 2 baking sheets. Place 1 baking sheet on oven rack 3 inches from heat; broil 10 minutes. Carefully turn nests over, and broil 6 minutes or until golden brown. Set aside. Repeat procedure with remaining nests.
To prepare the sauce, combine broth and next 5 ingredients (broth through soy sauce); stir well with a whisk. Set aside.
To prepare vegetables, heat 2 teaspoons vegetable oil in a large nonstick skillet over medium-high heat. Add ginger and garlic; stir-fry 10 seconds. Add leek, carrot, and mushrooms; stir-fry 2 minutes. Add sauce; bring to a boil, and cook 2 minutes or until thick. Stir in sprouts; cook until thoroughly heated. Spoon vegetables over nests.