One of my friends had an impressive medlar tree of great age so I looked in some Bookes to find out what to do with them. We picked (and picked up!) the medlars late in the year (November), and put them on trays indoors to 'blet' in time for Dec/Jan eating. Bletting is the process where they go brown and spongy and sweet (and a good word for Scrabble). Then we'd squeeze out the gloop and eat with ice cream :P :D.
If anyone wants to know the Olde Englishe slang for medlars, based on the shape of their calyx end, it's just too rude to post here, sorry ;D