1. First, prepare the pumpkin purée for the filling. Remove the seeds and stringy centre from the pumpkin, then peel away the skin as thinly as possible. Cut the flesh into small cubes. Heat the butter in a frying pan, add the pumpkin with 25g of the sugar and cook for about 10 minutes until softened. Transfer to a food processor and work until smooth. Allow to cool. You can make this purée a day or so ahead and freeze it to concentrate the flavour.
2. For the sponge base, preheat the oven to 200C/400F/gas mark 6. Whisk the egg whites in a bowl until softly stiff. Gradually fold in the caster sugar, then the egg yolks. Sift the cornflour and flour together over the mixture and then fold in carefully.
3. Line a baking sheet with baking parchment. Spread the sponge mixture out to an area approximately 30cm square it needs to be an even thickness, but not necessarily a neat square. Bake for 710 minutes until golden brown and springy when pressed. Invert on to a wire rack to cool and then peel off the paper. Lower the oven setting to 170C/325F/gas mark 3.
4. For the cheesecake you will need a 2324cm springform cake tin about 6cm deep. Cut out a round from the sponge base to fit exactly inside the tin, using the base of the tin as a guide. It is preferable to cut the sponge a little larger and trim it to fit, rather than cut it smaller and leave gaps that the pumpkin filling might leak through.
5. For the filling, beat the mascarpone, crème fraîche, soured cream, 50g of the remaining sugar, the vanilla seeds (or extract) and 2 egg yolks together in a bowl until evenly blended. Stir in the pumpkin purée.
6. Whisk the 2 egg whites in another bowl until softly stiff. Gradually whisk in the remaining 25g sugar and gently fold into the pumpkin mixture. Pour the filling over the sponge base in the tin and bake for 4050 minutes until lightly firm on top.
7. Leave the cheesecake to cool and then chill in the tin. Run a table knife around the inside of the tin and carefully unmould on to a flat plate. Serve in wedges, dusted lightly with icing sugar.