2 sticks plus 2 tablespoons (9 ounces) unsalted butter, softened
1 large egg
2 large egg yolks
1 teaspoon pure vanilla extract
In a medium saucepan, combine the figs with the water, sugar, cinnamon, nutmeg, cloves, lemon juice and zest and a pinch of salt and bring to a boil. Simmer the figs over moderately low heat until tender and the liquid is thick and syrupy, about 40 minutes. Transfer the mixture to a food processor and puree. Let cool.
In a food processor, pulse the pistachios until finely ground. Transfer the nuts to a large bowl and add the flour, sugar, baking powder and lemon zest. Add the butter and stir with a wooden spoon until combined; it may be necessary to knead the dough with your hands. Add the whole egg, egg yolks and vanilla and stir or knead until evenly combined. Break off one-third of the dough and flatten it into a disk. Pat the remaining dough into another disk. Wrap both pieces in plastic and refrigerate until chilled, about 30 minutes.
Preheat the oven to 350°. Spray an 11-inch fluted tart pan with a removable bottom with vegetable oil cooking spray. Press the larger disk of dough into the bottom and up the sides of the tart pan to form an even 1/4- to 1/3-inch-thick crust. Trim off any excess. Spread the fig filling over the crust. Roll out the smaller disk between 2 sheets of wax paper to a 12-inch round about 1/4 inch thick. Remove 1 sheet of the wax paper and invert the top crust over the filling. Press the edges together to seal and trim off any excess. Chill the tart for 15 minutes.
Bake the tart in the center of the oven for 50 minutes, or until golden, covering the top with foil if the edge becomes too brown. Let the tart cool for 30 minutes, then carefully remove the fluted ring. Let the tart cool completely before serving.
The tart can kept in an airtight container at room temperature for up to 2 days.