With a sharp knife, cut the mushrooms on the diagonal into quarters, depending on the size. Prepare the seasonings and set by the stove.
Heat a wok or a heavy skillet until very hot, add 1 teaspoon of oil and heat until hot. Add the snap peas, minced garlic, rice wine or sake, and salt, and toss lightly over high heat for about 1 1/2 minutes until the peas are just tender (snow peas will take slightly less time.) Remove from the pan and arrange around the outside of the serving plate.
Reheat the pan and the remaining oil until very hot. Add the Seasonings and stir-fry about 10 seconds until fragrant. Add the mushrooms and toss lightly with a spatula or shovel over high heat for about 1 minute. Add the sauce and toss lightly to thicken, stirring constantly to prevent lumps. Arrange the mushrooms inside the snow peas on the serving platter. Serve immediately.