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In this photo: The 2 fruits at the far left are fuyu, or maybe not true fuyu but the flat kind of persimmon sometimes called an 'apple' persimmon because you don't need to wait til it's ripe to eat. This is the crunchy yummy that can find it's way into salads in the fall. The next two fruits that are oval-ish are hachiya: the traditional persimmon that you must wait to ripen: it needs to be runny like an egg yolk before you can cook it. The three darker orange persimmons are what I have waiting for me right now: ripe hachiyas! I cut them open with a sharp knife and then push as much pulp as I can through a sieve. This is what I get.
Lots more persimmon information.
Recipe confession: I don't have a favorite persimmon recipe. Every fall I see the harvest waiting to be cooked up and I find the most convenient recipe I can on google that matches what ingredients I have one hand.