Chop the quinces roughly and place in a large saucepan. Cover with water and bring to the boil, then reduce the heat and simmer for 30 minutes until soft.
Push the mixture through a sieve, then weigh the purée (it should make about 1 kg/2 lb). Return the purée to the pan with an equal amount of granulated sugar. Stir until dissolved, then simmer for about 40 minutes or until thickened and a clean line appears when you scrape through the mixture at the bottom of the pan with a spoon.
Pour into lightly oiled sterilized containers and store in the refrigerator until just set. Store for up to 6 weeks.
Cut the cheese into thick triangular slices to serve. Spoon the membrillo on top of the cheese and arrange on serving plates.