In the bowl of a food processor outfitted with a blade attachment, pulse the confectioner's sugar and flour to combine. Add the cubed butter, processing until broken down to the size of sand. Add in the egg and process until it comes together. Transfer the pate sucree dough to a sheet of plastic wrap. Chill for 30 minutes or until still pliable but not soft. Meanwhile, start the cocoa spread recipe.
Make the Fig Cocoa Spread
Combine sugar, water, brewed coffee, figs, cocoa powder, and salt in a heavy-bottomed saucepan set over medium heat. Cook and stir for 7 minutes or until sugar has dissolved. Strain figs into a food processor, reserving syrup. Process figs with 1/2 cup syrup until smooth. Using a spatula, transfer figs back to the saucepan. Over medium low heat, stir in remaining syrup with a wooden spoon, cooking for 3 minutes or until integrated.
Create the Tarts
Adjust oven rack to the middle. Preheat the oven to 350°F. Pull out tart pans and cut parchment paper squares that are bigger by an inch or two from the tart pans.
Roll out chilled tart dough to 1/4-inch thickness, cutting out 6-inch circles of dough. Re-roll dough to cut out remaining circles, reserving scraps. Press dough circles into the tart pans. Place parchment into each tart pan and fill with pie weights or dried beans. Blind bake for 15 minutes. Remove the bean-lined parchment and bake for 5 minutes more.
Fill each par-baked tart crust 3/4 of the way full with fig cocoa spread. Bake for 15 minutes more. Cool on a wire rack for 20 minutes.
While the tarts are cooling, whip heavy cream to medium peaks to dollop on the tarts. Garnish with chocolate-dipped figs, figcolates, or sift on confectioner's sugar if desired.