This is quince cheese or membrillo in Spanish.  Here is how I made it.
Take  as many quinces as you have at hand (I only had a couple).  Wash but don't peel them.  Chop the quinces roughly and put them in a pan, skins, seeds, core the whole lot.  Add enough water to barely cover the fruit.  Simmer gently for about 30 minutes until soft.
Mash or puree in a food processor, then press it through a sieve to get rid off the seeds and grainy parts.
Weigh the pulp, put it in a heavy-bottomed pan and add sugar equal in weight to the pulp.  Bring to the boil to dissolve the sugar, then reduce the heat to minimum and simmer for 1-1.5 hours.  It will spew and bubble like a hot geyser and turn a beautifully glossy deep amber colour.  It will also fill your kitchen with a refreshing fruity aroma.
When it's ready your spoon will leave a clear channel on the bottom of the pan for a couple of seconds.  I like to pour the mixture in a shallow tray, lined with baking parchment, to a depth of about 3cm.
Leave it to set overnight, then turn it out, wrap in greaseproof paper or baking parchment and keep it in a cool place or fridge for about a year.  It goes wonderfully with cheeses (traditionally Spanish Manchego), cold meat or you could bake it into cakes.

gnarled fruit

setting in the tin

deep amber colour