Preheat oven to 350 degrees. With an electric mixer, beat together butter, sugar, vanilla, and egg until creamy. On low speed, add flour, almonds, and salt, and continue to mix until dough starts to form. Using your hands, shape the dough into a disk and then wrap in plastic. Refrigerate for about 15 minutes.
Roll out the dough to ¼ inch thickness on a floured surface. Cut out cookies using a cookie cutter. For half of the cookies, use a smaller cutter to cut out the center. Place cookies on an ungreased baking sheet and bake for 8-10 minutes, or until golden brown. Cool on a cooling rack.
For the glaze: Whisk together room temperature mascarpone, maple syrup, and powdered sugar until smooth. Add a bit of water to thin out mixture, if necessary.
To assemble the cookies: Drizzle glaze over cookies with cutouts. Spread fig jam in a thin layer on the flat side of whole cookies. Sandwich flat sides of the whole cookies with the cutout cookies, allowing the jam to show through the center.