In a large bowl, use an electric mixer to combine the butter, powdered sugar, almond extract and salt. Beat until creamy. Add the flour, mixing at low speed, until well-combined.
Divide the dough in half, flatten into two disks and wrap each disk in plastic wrap. Refrigerate for one hour, or until firm.
Preheat the oven to 350℉. Line baking sheets with parchment paper or silpat mats.
Roll out a disk of chilled dough on a lightly floured surface to ¼-inch thickness. Cut with 2-inch heart cookie cutters. For HALF of the cookies, cut out the center of each heart with a smaller heart cookie cutter. Place the cookies 1-inch apart. Bake 7 to 9 minutes, or until the edges are lightly browned. Cool for a few minutes, andthen move to a rack to cool completely. (If you want to bake the mini cut-out hearts, you can bake those too for about 6 minutes).
Place the cookies with the center cut out onto waxed paper. Sprinkle the cookies with a dusting of powdered sugar. Spread the whole heart cookies with jam- just about ¼ to ½ teaspoon. Top with the cut-out cookie (powdered sugar side up).