Peel and seed the ripe Hachiya persimmons.
Mash the pulp until mostly smooth.
Add persimmon pulp, sugar, and lemon juice to a heavy-bottomed saucepan.
Cook over medium heat until the mixture begins to bubble and the sugar has dissolved.
Reduce heat to medium-low and simmer uncovered for about 20–25 minutes, stirring regularly.
Test the jam on a chilled plate. If it wrinkles and holds its shape, it is ready.
If necessary, continue cooking for another 5 minutes and test again.
Stir in vanilla and cinnamon during the final 2 minutes, if using.
Transfer the hot jam to clean, sterilized jars, leaving about ½ inch (1cm) headspace.
Cool to room temperature before sealing and refrigerating.