For garlicky sweet shitake mushrooms: Slice caps in 1/4' slices. Heat vegetable oil over medium heat and add mushrooms and garlic. Cook, stirring constantly, for 5-8 min. until gills begin to brown. Add sherry, stirring constantly until it evaporates. Add the sweet soy sauce stirring and tossing until they are completely coated. Remove and cool.
For Ginger Miso dressing: Combine all ingredients except oil in blender. With blender running drizzle in oil. Add 1/4 Cup water to thin and blend until smooth.
For salad: Segment grapefruit and set sections aside. Peel and pit avocado and cut into 1/4' slices. Toss with a bit of grapefruit juice to prevent discoloration.
Toss daikon, grapefruit and salad greens in bowl. Drizzle with 1/4 Cup dressing and gently mix to coat.
Divide salad on chilled salad plates and top with avocado slices, pomegranate seeds and garlicky sweet shitake mushrooms. Top with additional dressing as desired.