Line a baking tray with baking paper. Fit a piping bag with a medium, round nozzle and set aside.
Place the ground almonds and icing sugar into a food processor. Pulse 10 times, then sift into a large bowl, discarding any bits of almond that do not pass through the sieve. Add 1 of the 15g portions of egg white to the almonds/sugar and mix well to form a paste. Set aside.
Place the other 15g portion of egg white into the clean, metal bowl of an electric stand mixer, fitted with the whisk attachment. Put the caster sugar and water into a small saucepan and place over medium heat. Use a candy thermometer to measure the temperature of the syrup.
When the syrup reaches 112-114°C, start mixing the egg white in the bowl of the stand mixer on high speed. When the syrup reaches 118°C, remove it from the heat and pour it down the side of the bowl, into the egg white (which should be at soft peaks). When you have added all of the syrup to the bowl, turn the mixer up to full speed and whisk until the meringue reaches stiff peaks. When the meringue is ready, the outside of the bowl should only have a slight hint of warmth, when touched.
Add 1/3 of the meringue to the almond paste and, using a metal spoon, mix it in thoroughly until well combined. Add the rest of the meringue and fold it in, using a figure of eight motion, until the mixture is cohesive and comes off the spatula in ribbons (if you leave those ribbons for 30 seconds, they should settle back into the mixture). Do not overmix at this stage.
Place the macaron mixture into the piping bag. Hold the piping bag vertically and pipe your shells, leaving plenty of space between each one. You will need 12x 3.5cm diameter shells and 2x 4.5cm diameter shells.
Once you have piped your macarons, lift the tray slightly and tap it down on the surface a couple of times, to raise any air bubbles to the surface. Use a small, sharp knife or cocktail stick to pop any remaining bubbles, allowing the mixture to fall back on itself. Set the macarons aside to form a skin- about 30-40 minutes on a dry day, longer if it is more humid. The macarons will be ready when you can gently touch the surface of the macarons, without any batter coming off on your finger.
While the macarons are forming a skin, preheat the oven to 165°C fan. Bake the macarons for 11 minutes, or until you can gently wiggle your finger on top of the shells without them wobbling independently from their feet. Remove the macarons from the oven and let them cool completely on their tray before decorating.