Snap tough stem ends off asparagus. Cut spears at a 45° angle into 1/2-inch-thick slices. In a small bowl, mix broth, soy sauce, cornstarch, and white pepper.
Set a 14-inch wok or 12-inch frying pan over high heat. When hot, add oil, ginger, and garlic; stir until garlic begins to turn golden, about 30 seconds. Stir in asparagus and add 3 tablespoons water; cover and cook just until asparagus is bright green, 1 to 2 minutes. Add shrimp and stir, uncovered, until they are opaque in center of thickest part (cut to test), 2 to 3 minutes.
Stir broth mixture and add to pan; stir until sauce boils and thickens. Add salt to taste.
Set a noodle pillow on each of four dinner plates. Spoon shrimp and asparagus stir-fry equally over noodle pillows.
Making noodle pillows:
In a 5- to 6-quart pan over high heat, bring 3 quarts water to a boil. Add 12 ounces dried thin Asian wheat noodles or dried vermicelli pasta and stir to separate. Cook until barely tender to bite, 3 to 7 minutes. Drain and return to pan. Mix in 2 tablespoons Asian sesame oil and salt to taste.
Divide noodles into four equal portions; set each mound about 2 inches apart on two 10- by 15-inch nonstick baking pans. Pat each into a 1/2-inch-thick round.
Bake pillows in a 425° oven until most of surface is crisp and browned, 15 to 20 minutes (switch pan positions halfway through baking). Serve hot.