Place pistachios and sugar in bowl of food processor and pulse until finely ground.
Add 1 egg, 4 Tablespoons unsalted butter, 2 teaspoons of flour and 1/4 teaspoon of pure vanilla extract.
Remove the stems and slice the figs into 4 quarters.
In a mixing bowl, gently stir the figs together with 1 Tablespoon fresh lemon juice.
Unroll refrigerated pie crust on lightly floured parchment paper that is placed on a flat baking sheet.
Spread pistachio datil pepper cream filling in the middle of the pie crust, leaving about a 2 inch border along the outside edge.
Place fig sections, skin side down on the pistachio filling, creating a flower or star bust design.
Gently fold over outside edges of pie crust onto the outermost ring of figs, pleating as necessary to form a rustic circle with the dough.
In a small bowl, beat the remaining egg with 1/2 teaspoon of water. Using a pastry brush, brush the egg wash on the outside edges of the pie crust.
Sprinkle with 1 teaspoon granulated sugar, if desired.
Bake the tart at 350 degrees F for 30 minutes.
Place strips of aluminum foil along the outer edges of the pie dough to prevent burning. Return to the oven for another 30 minutes.
Remove tart from the oven and allow to cool for at least 30 minutes.
Serve with freshly whipped cream or good quality ice cream if desired.