To make the batter: Put the batter ingredients into a medium bowl and whisk until smooth.
Pour the oil into a medium-small saucepan over high heat. When the oil is hot (drop in it a few drops of the batter, if it sizzles and bubbles, it's hot) lower the heat to medium-high.
Frying: dip the veggies in the batter then place them gently in the hot oil. Fry for 1 minutes then, using a metal tongs, flip and fry the other side until it's tan. Remove from the oil and place on a plate lined with a paper towel.
Dipping sauce: put the Combu and mushrooms in a small saucepan with 1 cup of water and bring into a boil. Stir in the soy sauce and Mirin (or rice vinegar) and continue to boil for 2-3 minutes. Remove from the heat and let it cool. Serve in a small bowl on the side with the tempura.