Step 1Make the persimmon puree: In a blender, puree the persimmons (with skins), adding simple syrup to taste. This makes about one-half cup puree. The puree will keep, covered and refrigerated, for up to 1 week.
Step 2Prepare a martini glass by placing 1 part cinnamon and 3 parts salt (taste and adjust ratio as desired) on a small plate, wet the rim of the glass with a lime wedge, then dip it in the mixture. In a cocktail shaker with ice, combine the tequila, 1 1/2 ounces of persimmon puree and lime juice. Shake vigorously and strain into the rimmed glass. Garnish with a lime wheel.