Whisk the flour, baking powder, confectioners' sugar, cinnamon, and salt in medium a bowl; set aside.
Add the butter and granulated sugar to the bowl of a stand mixer fitted with the paddle attachment. Beat on medium speed until fluffy. Mix in the vanilla extract and the egg. Reduce speed to low and add flour mixture, mixing until just combined. Cut the dough in half and shape it into 2 disks. Wrap the disks in plastic wrap and refrigerate for at least 2 hours.
Preheat oven to 375° F. Line two baking sheets with parchment paper.
Working with 1 disk at a time, roll out dough on a lightly floured surface to ⅛-inch thick. Cut out dough with a 2-inch fluted cookie cutter. Cut out centers of half the cookies with a ½-inch heart cutter. Re-roll the scraps and cut out additional cookies. Space the cookies 2 inches apart on baking sheets. Chill dough on baking sheets for 5 minutes.
Bake cookies and hearts until pale golden, 8 to 10 minutes, rotating the pans 180° halfway through the baking time. Transfer the pans to wire racks to cool and allow the cookies to cool completely on the pans before transferring to a work surface for the next steps.
While the cookies are baking, heat the jam in a small saucepan over medium heat until reduced and thickened, about 7 minutes; let cool.
Dust the cutout cookies with confectioners' sugar - these will be the tops of your cookie sandwiches. Spread jam onto uncut cookies; top with the cut out cookies.