Preheat the oven to 180°C/350°F/Gas mark 4.
Melt the butter in a pan, and stir in 25g/1oz of the caster sugar and the biscuit crumbs, mixing thoroughly. Press the mixture over the bottom of a 20cm/8in round springform cake tin and chill while preparing the filling.
Beat the cream cheese until smooth. Beat in 350g/12oz of the sugar, then gradually add the cocoa powder, 1 teaspoon of the vanilla essence and the eggs. When smooth, pour into the crumb crust, and bake for 35 minutes.
Combine the sour cream with the remaining sugar and vanilla essence. Spread the mixture over the top of the cheesecake, and bake for another 10 minutes. Remove from the oven, cool and chill overnight.