Make the paste: Line 3 baking sheet trays with baking parchment paper, and brush with coconut oil.
Trace a spiral design onto 1 piece of parchment. On the other, trace slightly diagonal lines of about three-quarters of an inch wide, leave the third plain.
Cream the butter and sugar until light and fluffy. Then gradually, add the egg whites, beating well between each addition. Sieve the flour into the mixture, and fold in.
Divide into 6 small bowls, placing roughly half a cup in each bowl. In each bowl, mix in the food colouring, until you have rainbow colours. Place each colour into a piping bag, and pipe the paste onto your parchment paper. You may need to use a paintbrush to completely cover the design. (You don’t want air bubbles in the design.)
When finished, put the parchment paper into the freezer until required.
Make the cake: Preheat the oven to 425 F.
Whisk the egg whites until they form soft peaks. Add the granulated sugar, and continue whisking until medium-stiff peaks are formed.
While the egg whites are whipping, in a separate bowl, beat the almonds, confectioners sugar, vanilla, and eggs for 5 minutes, until the mixture is light and fluffy. Sieve the flour into the mixture. Then use the electric whisk to beat into the mixture until just combined. Gently, fold in the meringue mixture using a metal spoon. Next, gently, fold the melted butter into the mixture. Split the mixture evenly between 2 bowls. You may find the scales helpful here!
Remove the colourful designs from the freezer, and place into the baking trays. You will have 2 patterned trays and a third plain tray. Pour a third of the mixture over each tray, and smooth with an offset spatula.
Bake for 5 to 8 minutes, until the cakes are cooked and springy to the touch.
Turn out each cake onto a clean tea towel, and peel off the paper. Leave to cool.
When cooled, cut strips of the rainbow striped cake to line the sides of a 7-inch springform cake pan, ensuring the pattern is facing outwards against the sides of the tin. Cut a circle out of the middle of the spiral cake to line the top. Set aside. Cut a second circle to make the bottom of the cake, and start to line the bottom. You will have to use offcuts of the cakes you have just cut. Cut 2 circles out of the plain cakes, and set aside.
To assemble: Place a third of the whipped cream into the bottom of the cake. Then, top with the strawberries, and place 1 of the plain cake circles on top. Next, repeat the layering process, adding a third of the cream, the blueberries, and the second circle of plain cake. Finish with the final third of cream and the raspberries, then place the patterned cake circle, pattern side on top.
Place the cake in the fridge for at least 4 hours to set.
When ready to serve, pipe with whipped cream, and decorate with sprinkles.