For the tempura, place the ice cubes and flour into a large bowl and then gently whisk in enough water to make a thick batter with the consistency of double cream. (You may not need all of the water.) Season with salt and freshly ground black pepper.
Pour the vegetable oil into a large saucepan or deep-fat fryer and heat until a small cube of bread dropped in sizzles and turns golden in 30 seconds. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
Dip the chicken pieces and courgette batons into the batter, then carefully lower into the hot oil in small batches. Deep-fry for 3-4 minutes, or until golden-brown and the chicken is cooked through. Remove with a slotted spoon and drain on kitchen paper.
For the dip, place all of the dip ingredients into a small saucepan and simmer gently for 4-5 minutes, stirring occasionally, or until thickened slightly. Pour into a small bowl for dipping.
To serve, pile the tempura onto a serving plate and serve with the tomato chilli dip on the side.