Stamp out a circle of Madeira cake using a small chef's ring and keep it inside the ring.
Whisk the double cream until soft peaks form, then whisk in the mascarpone and sugar.
Stir in the lemon zest, lemon juice, and chopped apricots.
Spoon the mixture into the ring over the cake and smooth with a palette knife.
Chill in the refrigerator until the mixture is set.
Release the ring by warming the outside with a blow torch and top with raspberries.
Blend the apricot syrup and remaining apricot halves in a food processor until smooth.
Serve the cheesecake with the apricot purée and a garnish of mint.