Grind the chocolate biscuits and 75g of chocolate in a food processor; the crumbs should be small. Mix in 3 tablespoons of sugar.
Melt 7 tablespoons of butter or margarine, and add it to the chocolate crumbs. Press into the bottom of a 23cm spring form cake tin.
Melt 340g of chocolate, and cool slightly. Blend in cream cheese, 350g sugar, eggs, 125ml cream, cocoa, vanilla and peppermint extract.
Pour this over the biscuit base. Bake for 1 hour at 180 C / Gas 4. Cool overnight.
In a small bowl, mix together the soured cream and 4 tablespoons sugar. Pour on top of cooled cheesecake. Bake for 20 minutes at 180 C / Gas 4. Chill for 6 to 8 hours.
To decorate the cheesecake make a chocolate icing: In a small saucepan, simmer 125ml cream and 1 tablespoon butter. Add to this the 170g of chocolate, and stir until melted. Remove from heat.
Freeze until the mixture is piping consistency (stir occasionally). Using a pastry bag, pipe a lattice design on the top.