Cream butter, and powdered sugar until fluffy. Add egg and vanilla extract, then gradually add flour. Mix until combined.
Press dough into a tart shell and refrigerate for at least an hour, or overnight. Preheat the oven. Poke holes in the crust with a fork and blind bake.
Meanwhile, slice persimmons into thin half-moons. Set aside the smaller pieces for the center of the tart.
Spread persimmon puree over the bottom of the baked tart shell.
Arrange persimmon slices in overlapping concentric circles, starting from the outside and working inward.
Sprinkle sugar over the persimmons, making sure some sugar gets between the slices. Bake until the persimmons soften.
Cool the tart slightly, then brush with warmed jam. Chill the persimmon tart briefly before serving.