Make the dipping sauce by combining the ingredients and whisking until the dashi is dissolved.
Make the batter by beating the water and egg yolks together, then whisking in the flour until just combined.
Heat the oil in a wok, deep fryer or saucepan until very hot but not smoking. Dip vegetable pieces in the batter and drop in the hot oil. Work in batches so you don't overcrowd the pan and cool the oil.
Remove the veggies from the oil when they are golden brown and drain on paper towels. Serve with the dipping sauce.