Heat peanut oil in a large skillet. Add mushrooms and scallions and sauté for 2 to 3 minutes. Add ginger, garlic and sprouts. Stir-fry for 2 minutes. Remove to a large bowl.
Add ¼ pound mashed tofu to bowl. Stir flour and baking powder together and sprinkle into bowl. Toss until all ingredients are well coated. Set aside.
Blend all batter ingredients together until smooth, preferably using a food processor.
Add batter to flour-coated vegetables and mix well.
Spoon mixture onto well-oiled baking sheets, forming 10 patties about 4-inches wide and ½-inch thick.
Bake at 350ᵒ F. for 20 minutes. Remove from oven, flip with a spatula, and bake for 10 more minutes. Combine first 5 ingredients in a saucepan and bring to a boil. Reduce heat to low. Stir cornstarch and cold water together in a small bowl. Add to saucepan and bring to a low boil. Reduce heat and simmer, stirring constantly, until thickened.
Arrange patties on a serving platter and cover with heated sauce.