Preheat the oven to 350 degrees.
Line a baking sheet with parchment paper. Place the flour, butter, blue cheese and a few grinds of black pepper in the bowl of a food processor. Process until the dough just comes together and starts to form a ball. Dump the dough onto a lightly floured surface and knead a few times to pull the dough together.
Roll out to 1/8 inch thick with a floured rolling pin. Cut rounds out of the dough with a floured 1-inch cutter and transfer the rounds to the parchment-lined baking sheet. Using the back or a round half-teaspoon measure or your knuckle, make an indention in the top of each dough round. Spoon about ¼ teaspoon of fig preserves into each indention, using your finger to push the preserves as best as possible into the indentions.
Bake the savories for 10 14 minutes, until the preserves are bubbling and the pastry is light golden on the bottom. Let cool on the baking sheet for at least 10 minutes, the remove to a wire rack to cool. Youll find fig preserves at the grocery it may be shelved with the fancy jams and jellies. You can make these a day ahead and keep them in two layers separated by waxed paper in an airtight container.