Adjust oven rack to middle position and heat oven to 375 degrees. Make foil sling for 8-inch square baking pan by folding 2 long sheets of aluminum foil so each is 8 inches wide. Lay sheets of foil in pan perpendicular to each other, with extra foil hanging over edges of pan. Push foil into corners and up sides of pan, smoothing foil flush to pan. Grease foil.
Pulse 1 cup flour, 2 tablespoons sugar, and butter in food processor until mixture resembles wet sand, about 10 pulses. Transfer mixture to prepared pan and press firmly into even layer. Bake until light golden, about 15 minutes. Let cool completely in pan.
Place pistachios in zipper-lock bag and tap them with meat pounder until crushed. Toss figs, coconut, and pistachios together in bowl, breaking up any clumps. Whisk egg, maple syrup, vanilla, salt, remaining 2 tablespoons flour, and remaining 1 cup sugar together in large bowl. Fold in pistachio mixture, then spread evenly over cooled crust.
Bake bars until deep golden brown and set, 20 to 25 minutes. Let bars cool completely in pan on wire rack. Using foil overhang, lift bars out of pan. Cut into 9 squares and cut each square diagonally into 2 triangles.
Microwave chocolate in small bowl at 50 percent power, stirring occasionally, until melted, 30 to 60 seconds. Dip 1 corner of each triangle in melted chocolate and place on parchment paper–lined baking sheet. Refrigerate triangles until chocolate is set, about 30 minutes, before serving.