Preheat the oven to 150°C/fan 130°C/gas mark 2. Line 2 baking trays with non-stick silicone paper or baking parchment. Whizz the icing sugar and ground almonds to a fine powder in a food processor. Sift evenly into 3 separate bowls and add different colouring to each.
In a separate bowl, whisk the egg whites with the cream of tartar until medium peaks form. Slowly add the caster sugar, one spoonful at a time. Add the vanilla extract and whisk until thick and glossy.
Slowly fold one-third of the meringue into each of the bowls containing the almond mixture until completely combined. Keep folding until the mixture deflates and creates a ribbon effect for about 20 seconds when it falls from the spoon.
Spoon into 3 separate piping bags, each fitted with a 1cm plain nozzle. Pipe small equal rounds – about 3cm each, spaced 2cm apart – on to the baking trays. Tap the baking trays hard several times to remove any bubbles and flatten the macaroons. Allow to stand for 20 minutes to form a slight skin, then cook the macaroons in the middle of the oven for 20 minutes.
Meanwhile, beat the butter until light and fluffy, then beat in the icing sugar. Spoon the mixture into 3 small bowls and stir a different colouring into each. Use the buttercream to sandwich together pairs of macaroons before serving.