Soften shiitake mushrooms in water for 45 minutes. Squeeze the water out with your hands and pat dry. Remove stems and discard them.
Wash shrimp, remove shells, devein, and chop into small pieces. Add salt, chopped green onions, and seasonings. Mix well.
Dust the inside of one mushroom with cornstarch and put 1/4 of the shrimp mixture on top. Dust the inside of another mushroom and put it on top of the filled mushroom. Continue to make four mushroom sandwiches.
Mix the batter ingredients.
Dust each mushroom sandwich with flour, plunge into batter, and deep fry in heated oil over medium heat until batter turns slightly golden. Serve hot with tempura dipping sauce of your choice.