Sift the flour, baking powder and salt into a medium bowl. Beat the butter and sugar in a large bowl with a mixer on medium-high speed until light and fluffy, 3 to 5 minutes. Add the egg and vanilla; beat until combined. Reduce the mixer speed to low; add the flour mixture in 2 batches, beating after each, until just incorporated. Divide the dough between 2 sheets of plastic wrap; form into disks. Wrap and refrigerate until firm, at least 1 hour.
Make the filling: Bring the heavy cream to a simmer in a small saucepan over medium heat. Pour over the chocolate in a medium bowl and let stand 2 minutes; stir until smooth. Set aside.
Working with 1 disk at a time, roll out the dough between floured sheets of parchment paper until about 1/8 inch thick; chill 15 minutes. Line 2 baking sheets with parchment. Cut out circles with a 2-inch cutter; transfer to the baking sheets. Gather the scraps and refrigerate until firm; reroll once to cut out more cookies. Chill the cutouts 30 minutes.
Position racks in the upper and lower thirds of the oven and preheat to 350 degrees F. Bake, switching the pans halfway through, until just golden, about 12 minutes. Let cool 5 minutes on the baking sheets, then transfer to racks to cool completely.
Briefly beat the filling with a mixer on medium-high speed until thick, 30 seconds. Chill until cold, about 1 hour. Sandwich between the cookies and roll the edges in sprinkles.