Preheat the oven to 180C/350F/Gas 4. Grease and line a 23cm/9in springform cake tin with baking parchment.
For the baked blueberry cheesecake, melt the butter in a medium saucepan and add the crushed biscuits and mix.
Tip into the prepared tin and press the crumbs down firmly and evenly to form a bottom crust. Bake for 10 minutes, then set aside to cool completely.
Place the vanilla seeds, lemon zest and juice, caster sugar, cornflour, cream cheese and cream in a large glass bowl and whisk together.
Add the eggs continually whisking until the mixture is smooth, then add the blueberries and stir carefully.
Pour onto the baked base and tap the tin lightly against the work surface to settle the mixture into the tin. Wrap the outside of the tin in a double thickness of foil if you are concerned about the tin’s water-tightness.
Place the cake into a deep roasting tin containing 2cm/1in hot water.
Bake in the oven for 1¼-1½ hours or until the cheesecake is golden-brown and just set.
Turn the heat off in the oven and leave the cake in the oven for at least two hours or preferably overnight.
For the blueberry compôte, place the blueberries and sugar into a sauce pan and cook until the sauce thickens.
Serve the cooled cheesecake in slices with the blueberry compote.