Prepare the dip by combining teriyaki sauce, ginger and green onion. Refrigerate until needed. Heat the oil in a deep-fat fryer to 350 degrees F. Preheat the oven to 200 degrees F. Set a wire-rack over a baking sheet. To prepare the tempura batter, whisk together the water and egg yolk in a bowl. Add the flour and sugar and whisk until a thin, lump-free batter forms. Working in batches, dip the vegetables and mushrooms into the batter, draining away the excess. Deep-fry them until light golden, about 3 to 4 minutes. Set the tempura on the wire rack; keep warm in the oven until the rest are deep-fried. Arrange the tempura on a platter with the dip alongside.