Photograph: Dan Jones
Make the dressing first: put the ice cubes in a large bowl with some cold water. Set a small metal bowl in the middle of the icy water. Mix the vinegar, sugar and salt in a small saucepan. Set over a low heat and stir regularly until the sugar has dissolved, then pour into the chilled bowl. Once cool, set aside.
Put the rice in a large bowl and place in the sink. Cover the rice with cold tap water and, using your hands, gently agitate the rice until the water becomes milky in colour. Immediately pour off the water and keep repeating this process (about 10 times) until the water is almost clear. Drain into a sieve and leave for 30 minutes.
Place the rice in a medium-small saucepan that has a tight-fitting lid. Add 325ml soft mineral (or tap) water, cover and bring to the boil. Immediately reduce the heat and simmer with the lid on for 10 minutes. Turn off the heat and leave covered for 25 minutes.
Ideally, get someone to help you at this stage. Give them a fan or a folded newspaper. Spread the hot rice into a thin layer on a tray. Ask them to start briskly fanning the rice to help it cool quickly. As they fan, use a flat wooden spatula to toss the rice in horizontal, cutting strokes. You need to keep the grains separate, rather than mashing them together. As you toss, gradually sprinkle 2-3 tablespoons of the dressing over the rice. Check the taste as you do so, but take care, as you don't want mushy rice. Once the rice is tepid, it is ready for use.
Prepare your filling. Slice each of the king prawns in half lengthways, then in half widthways.
Sushi rice is very sticky, so you need to make 'hand vinegar' to prevent it from sticking to your fingers. Mix the rice vinegar and 3 tablespoons of water in a bowl. Place one sheet of nori shiny-side down on a bamboo mat. Moisten your fingers with a little of the hand vinegar and, using your fingertips, lightly spread a quarter of the sushi rice in a thin even layer over the nearest three-quarters of the nori sheet, up to the edge – leaving the furthest quarter of the sheet uncovered. You'll need to keep rinsing your fingers with the hand vinegar to stop them sticking.
Use your index finger to smear a very thin horizontal line of wasabi paste across the centre of the rice. Arrange the sliced prawns on top of the wasabi line. You'll need 3 prawns per piece. Try to make the filling an even thickness without any gaps or lumps, as this will ensure that it will look good when sliced. The thicker your filling, the thicker your roll.
To roll: Hold the line of ingredients firmly in place and, using your thumbs under the mat, gently lift up the nori and rice nearest to you and bring it over the filling, pressing it down as you continue to roll until you meet the end of the nori sheet. Hold the bamboo mat gently but firmly around the roll for 30 seconds to press the roll into shape.
Place the roll on a cutting board and remove the mat, making sure that the edge of the nori is underneath the roll. Repeat with the remaining ingredients to make 4 rolls in total.
To serve: Allow 1 roll (8 pieces) per person. Take a very sharp knife, wet the blade and slice the roll cleanly in half. Cut each half into 4 pieces, rinsing the knife between each cut. Place a dipping bowl filled with soy sauce on each person's plate, along with a small heap of pickled ginger. Arrange cut-side up on each plate and serve immediately.
Get ahead: sushi rice should be served at room temperature, so you need to make it about an hour before assembling your sushi.
Kitchen secret: for an alternative filling, cut ½cm-thick slices of very fresh, skinned raw salmon fillet into ½cm-wide strips. This filling can be combined with the cucumber, as we've done here. If you're nervous about using raw fish in your sushi, try using strips of smoked salmon instead.