Preheat the oven to 150°C/ 300°F/ Gas 2.
For the base: Roughly break up the digestive biscuits and put them in a food processor with the cocoa powder. Process until finely ground. Slowly pour the melted butter into the processor while the motor is running. Press this mixture into the base of a 23-cm springform cake tin greased and base lined with greaseproof paper. Press this mixture into the base of the prepared cake tin, using the ball of your hand or a tablespoon to flatten and compress it. Refrigerate while you make the topping.
Put the cream cheese, sugar and vanilla extract in a freestanding electric mixer with a paddle attachment (or use a handheld electric whisk) and beat on slow speed until you get a very smooth, thick mixture. Add one egg at a time while still mixing. Scrape any unmixed ingredients from the side of the bowl with a rubber spatula after adding the second and last eggs. The mixture should be very smooth and creamy.The mixer can be turned up to a higher speed at the end to make the mix a little lighter and fluffier, but be careful not to overmix otherwise the cheese will split.
Put the chocolate in a heatproof bowl over a saucepan of simmering water (do not let the base of the bowl to touch the water). Spoon a little of the cream cheese mixture into the melted chocolate, stir to mix then add a little more. This will even out the temperatures of the two mixtures. Eventually you can stir all the cream cheese mixture into the chocolate mixture until combined.
Spoon the mixture onto the cold base. Put the tin inside a deep baking tray and and fill with water until it reaches two-thirds of the way up the cake tine. Bake for 40 -50 minutes, checking regularly after 40 minutes.Don't overcook it should be wobbly in the centre. Leave to cool slightly in the tin, then cover and refridgerate overnight before serving.