Quince paste adds a floral note to these pointed cookies. Quince jam can be used for similar results.
Combine flour, sugar, and 1/2 teaspoon salt in the bowl of a mixer. Add butter, and beat on low speed until dough comes together, about 5 minutes. Shape dough into a disk, and wrap in plastic wrap. Refrigerate until firm, at least 2 hours.
Roll out dough to a 1/8-inch thickness on a lightly floured surface. Cut out forty 2-inch squares using a sharp paring knife and a ruler (alternatively, use a pizza cutter). Transfer to a parchment-lined baking sheet, spacing each about 1 inch apart. Refrigerate until chilled, about 30 minutes.
Meanwhile, pour boiling water over figs in a heatproof bowl. Let stand for 15 minutes. Puree figs in a food processor until smooth. Add quince paste, and pulse until combined.
Whisk together egg yolks and heavy cream in a small bowl. Working with a few dough squares at a time, cut a 3/4-inch slit into the 4 corners of each, and brush surface with egg wash. Fold the 4 corners of each square into the center to form a pinwheel, and gently press the center to adhere.
Preheat oven to 350 degrees. Spoon 1/2 teaspoon fig mixture into the center of each, and sprinkle entire cookie with sugar. Refrigerate for 30 minutes.
Bake until pale gold, 15 to 17 minutes. Let cookies cool on sheets set on wire racks for 10 minutes. Transfer cookies to racks, and let cool completely.
Dough can be refrigerated for up to 1 week or frozen for up to 1 month. Thaw before using. Quince-fig mixture can be refrigerated for up to 2 weeks. Cookies can be stored in an airtight container at room temperature for up to 3 days.