To make the tempura batter: mix together the corn starch, flour, salt and baking powder. Gradually add the water. Stir in the egg and immediately work the batter again. Mix in the shiitake mushrooms and cook in plenty of vegetable oil until crisp. Finely chop the chilli, roughly chop the coriander and mix with the soy sauce. Sprinkle the freshly grated lime zest and sesame seeds over the shiitake mushrooms. Serve with the dipping sauce.