Preheat the oven to 180 degrees C/350F and grease and line two 8 inch cake tins.
Place the milk chocolate into a heatproof bowl and place in the microwave for 30 seconds. Stir and return to the microwave in 10 second increments, stirring each time, until melted. Alternatively you can place the bowl above a small saucepan of simmering water and stir until melted. Leave to one side to cool.
Sift the flour, cocoa powder and baking powder into a medium sized bowl and mix until combined.
Place the butter and sugar into a large bowl or the bowl of your stand mixer and beat until light and fluffy, about 2 minutes on med-high speed.
Add in the melted chocolate.
Mix until well combined. Add in the vanilla extract and eggs and mix until well incorporated and smooth, about 1 minute on med-high speed.
Place the bicarbonate of soda and vinegar/lemon juice into a jug and mix briefly, it will foam up. Add in the buttermilk and beat with a fork for about 10 seconds.
Pour the buttermilk mixture into the cake mix and mix on med-high speed for about 1 minute until well combined and lovely and smooth.
Divide the batter between the two cake tins and smooth until level. Place in the oven for 45-50 minutes, until risen, golden and an inserted skewer into the centre comes out clean.
Leave to cool in the cake tins for at least an hour before transferring to a wire rack to cool completely.
Once the cakes are cooled, it's time to make the frosting. Place the white chocolate into a heatproof bowl and place in the microwave for 30 seconds, stir and return to the microwave in 20 second increments, stirring each time, until melted. Alternatively you can place the bowl above a small saucepan of simmering water and stir until melted.
Place the cream into a medium sized bowl and beat until soft peak, this means the cream will hold on a spoon for around 10 seconds before falling back into the bowl.
Place the butter, icing sugar, vanilla extract and melted chocolate into a large bowl and beat on slow until it begins to combine. Then turn the speed up to med-high and beat until smooth and fluffy, 2-3 minutes. Add in the whipped cream and mix until well incorporated, about 1 minute.
Place a small amount of frosting in the middle of a plate/cake board and then place one of the cake layers on top of it, top side up.
Place some frosting onto the top of the cake, enough to cover it, (which was about 2 good dollops with the spatula for me) and smooth with a small angled spatula.
Place the second cake layer on top of the frosted cake layer, bottom side up to ensure a smooth and level top. With the remaining frosting, frost the top and sides of the cake. For the side I always use a large flat metal spatula, whilst for the top I use a small angled spatula. You can either smooth the frosting or have a stippled effect like I went for this time. Once the whole cake is frosted, garnish with more chocolate, if desired!
Cake will keep in an airtight container, in the fridge, for 3 days.