Pour golden syrup into the base of a 1.5-litre pudding basin that’s been buttered, floured and lined on the base with baking paper. Arrange quince on top.
Melt chocolate in a bowl over a saucepan of simmering water. Beat butter, sugar and vanilla in an electric mixer until pale and creamy (2-4 minutes). Add flour, cocoa and baking powder, then egg and milk alternately, a little at a time. Add chocolate and beat until smooth. Transfer to prepared basin, smooth top and cover basin tightly with baking paper. Cover with a double layer of foil, secure with kitchen twine and place in a large saucepan with a cloth lining the base. Add boiling water to come halfway up sides of basin, cover with a lid and cook over medium-high heat, adding more water if necessary until puffed and pudding feels firm (2 hours).
For chocolate sauce, combine cream and butter in a saucepan, bring to the boil, then add chocolate and stir until melted and smooth. Keep warm (see note). Serve pudding hot with sauce and cream or ice-cream.
Note If the sauce cools, reheat gently over a saucepan of simmering water.