Rinse bok choy, and pat dry. Remove tough stems, and tear bok choy into 2-inch strips. Trim and discard stems from shiitake mushrooms. Wipe mushroom caps with a damp paper towel.
Sauté garlic, ginger, and onions in hot vegetable and sesame oils 30 seconds, stirring constantly. Add mushrooms, and stir-fry 2 minutes. Add bok choy, and stir-fry 2 minutes. Add snow peas, and stir-fry 1 minute. Add remaining ingredients; bring to a boil, stir-fry 1 minute, and drain. Serve at room temperature, or cover and chill up to 2 days.