Crust: In a stand mixer, cream the butter and powdered sugar together until light and fluffy. With the motor still running, add 1 ½ tablespoon of egg, the vanilla extract, and then slowly add the flours.Mix until the whole mixture is combined. Drop the pastry into the tart shell and press it into a 9" circular tart pan and evenly press it into the bottom and sides of the pan.Refrigerate the pastry in the tart pan for a minimum of 1 hour and up to overnight.
Preheat your oven to 375F. Poke fork holes in the crust and bake your chilled tart shell for 6-8 minutes.
In the meantime, cut the firm persimmons from their centers in 4 pieces. Stem side up, cut one face of the persimmon, rotate 180 degrees, and cut the other face. Then slice the two remaining sides leaving a rectangular core.
Slice them into very thin half-moons, approximately 1/8" thick. Do not use a mandoline since that tends to rip the pieces apart. Reserve the smaller pieces for the center of the rose.
Evenly spread the persimmon puree over the bottom of the tart shell.
Arrange the persimmon slices in concentric circles cut side down, overlapping each slice slightly. Work your way from the outside in toward the center, being sure to pack the rows tightly. You can roll the last few slices into a circle and tuck it into the center or just add a small dollop of the puree in the center.
Evenly sprinkle with the 2 tablespoons of sugar, and be sure to try to get some of the sugar between the persimmon slices.
Bake for 40-45 minutes until the persimmon soften. If the shell starts to over-brown, cover the edges with foil.
Cool for 10 minutes, preferably on a wire rack.
Heat some persimmon jam, apple jelly or apricot jam and gently brush a thin layer over the fruit tart with a pastry brush. Do not brush the jam on the crust. Pop the glazed tart in the refrigerator for 30 minutes before serving.
Notes
* You don't need to puree the persimmon if it's ripe enough. Instead, you can simply squish the persimmon pulp in your hand and spread it on the tart shell.The crust dough can be made up to 2 days in advance.