Beat together the butter and sugar until light. Add the egg and vanilla and mix until smooth. Add the mascarpone cheese and beat until smooth.

Sift together the dry ingredients and fold them into the butter mixture; mixing just until combined.

Wrap the dough in plastic wrap and refrigerate 1 hour.

Preheat the oven to 325 degrees F.

After the dough has chilled, place it on a lightly floured cutting board or counter and separate it into about three dozen portions. Roll each portion into a ball that is 1/2 inch in diameter and use the end of a spatula or wooden spoon to make a round indentation in the middle of each ball, flattening it slightly

Arrange the cookies on baking sheets that have been lined with parchment paper or ungreased silicone baking sheet liners designed to prevent cookies and pastries from sticking to baking pans.

Bake the cookies until they just begin to take on a golden color, then remove the baking sheets from the oven. Before the cookies have a chance to cool, spoon a small amount of fig jam into the indentation on each cookie. Once each cookie has its jam filling, allow the cookies to cool and the jam to set. Store in an airtight container.