For an exotic treat, I recommend a persimmon—that honeyed flavor and silky texture knock me out. Varieties include Fuyu, Sharon, and Hachiya. (Sharon persimmons are squatter, while Hachiyas are more heart-shaped.) While Fuyus and Sharons are ready to eat when slightly soft to the touch, Hachiyas aren’t ripe until they feel soft and almost mushy. All underripe persimmons will make your mouth pucker; they’re astringently tannic. Hasten ripening by stashing them in a paper bag with a ripe banana and leaving it on the counter for a day or two.
To eat a very soft persimmon, slice it open, scrape the pulp from the skin, and eat it with a spoon. If the fruit is firm enough to cut into slices, peel and serve simply, with a dollop of tangy crème fraîche. Or purée and strain the pulp; season it with lemon, lime, or orange juice, and freeze it into persimmon ice, or fold the purée into softly whipped cream for a persimmon fool.