Preheat the oven to 180℃, line an 8x8 inch baking tin with baking paper and set it aside.
To make the crumble add the brown sugar, granulated sugar, flour, walnuts, cinnamon, salt, butter in a bowl and stir together with a spoon until combined and lumpy. Set aside.
To make the cake add the butter into a large mixing bowl and break it up with a rubber spatula. Add the brown sugar and castor sugar, mix until combined. Add the eggs one at a time and beat well.
Add half the flour and fold together, pour in the buttermilk and mix until combined. Add the remaining flour, baking powder, baking soda, salt, cinnamon and chopped apples.
Fold together until combined, transfer half the mixture to the lined tin. Smooth it out and top with half the crumble mixture. Spread over the remaining cake batter and cover the top with the remaining crumble mixture.
Bake for 45-50 minutes until a tooth pick inserted into the center comes out clean. Let it cool down before frosting.
To make the frosting we brown the butter and let it cool for a few minutes. While it is still warm, add the white chocolate and stir until smooth, the mixture might look spilt but don’t worry it will come together. We then add the icing sugar and vanilla. Whisk until smooth. The mixture will look very loose - which is fine.
Add the whipping cream and beat it for a couple of minutes. You could do this with an electric beater but as it cools down the frosting will firm up. Once the mixture has thickened a little, place it in the fridge for a few minutes until it has firmed up and has become a spreadable consistency.
Top the cooled cake with the brown butter frosting and spread it evenly over the top. Make some swirls and slice it up.