1. Start by making the cake layer. Preheat the oven to 180oC, gas mark 4 and grease and line the 18cm cake tin with baking parchment.
2. Place the butter, sugar, flour and baking powder into the bowl of a stand mixer with paddle attachment. Mix on low until all the butter is rubbed into the dry mixture and it has a sandy texture.
3. In a small jug, beat together the milk, egg and vanilla. Pour the mixture down the side of the bowl into the dry ingredients and beat until everything is mixed together. When all the liquid has been added, beat on a high speed for 2 minutes until it is really well combined and smooth.
4. Pour the mixture into the prepared tin and bake in the preheated oven for 25-30 minutes until golden brown. Allow to cool completely on a wire rack. Cut in half horizontally.
5. To make the mousse, put the white chocolate into a large heatproof bowl over a pan of simmering water and heat until completely melted and smooth. Remove the bowl from the heat.
6. Pour 50ml of water into a small saucepan and sprinkle over the gelatine. Leave to soak for 5 minutes, then heat on low stirring until the gelatine has dissolved. Pour in 100ml of the double cream, stir to combine, then pour the gelatine/cream mixture into the melted chocolate along with the peppermint extract. Whip the remaining cream to stiff peaks using an electric whisk, then gradually fold in the slightly warm chocolate mixture until no large lumps of cream remain.
7. Take the 20cm springform tin and line the base and sides with clingfilm, trying to avoid too many creases. Cover the bottom with a thick layer of mousse. Lay half the cake over the top and cover with a layer of blackberries, then cover the whole cake with the remaining mousse and smooth over the top before adding the last layer of sponge, pressing it into the mousse. Freeze the whole cake for at least 1-1½ hours, or until very firm.
8. To make the mirror glaze, place the powdered gelatine and 60g of cold water in a small bowl and allow to bloom and absorb all the water. Combine 75ml water, the condensed milk and sugar in a heavy bottomed saucepan and bring to the boil. Remove from the heat and stir in the soaked gelatine, stir until gelatine has dissolved.
9. Place the white chocolate into a large bowl and pour the hot mixture over the top. Stir until melted and blend using a stick blender to remove bubbles. Remove half of the mix and stir in some pink food colouring, colour half of the remaining mix with blue food colouring, and leave the remaining mix white. Allow the glazes to cool to between 27-30oC before using.
10. Remove the mousse cake from the freezer and remove the tin. Upturn the cake onto the base of the tin so the mousse side is facing up. Position on a can over a baking tray. Dip a metal palette knife in a jug of boiling water and run it over the edges and top of the cake to give a smooth surface.
11. Mix together the glazes in a large jug to give a marbled effect, then pour over the centre of the cake. The glaze will run off the edge, down the sides and onto the baking tray. Chill until set then transfer to a serving plate and serve.