Whisk the flour, cocoa powder, 3/4 teaspoon salt and the baking powder in a medium bowl. Beat the sugar and butter in a large bowl with a mixer on medium-high speed until fluffy, about 3 minutes. Beat in the egg and 1 teaspoon vanilla. Reduce the mixer speed to low; beat in the flour mixture until just combined. Cover the dough and refrigerate until firm, about 30 minutes.
Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Line 2 baking sheets with parchment paper. Roll out the dough until 1/8 inch thick on a lightly floured surface, then cut out cookies with a 2-inch heart-shaped cutter. Arrange about 1 inch apart on the prepared pans. Bake, switching the pans halfway through, until the cookies are slightly firm, 8 to 10 minutes. Let cool 5 minutes on the pans, then transfer to racks to cool completely.
Make the filling: Combine the white chocolate, remaining 1/2 teaspoon vanilla and pinch of salt in a large bowl. Bring the heavy cream to a simmer in a saucepan, then pour over the white chocolate. Stir until smooth, then refrigerate until cold, 25 minutes. Beat with a mixer until creamy. Sandwich the white chocolate mixture between the cookies.
Photograph by Ryan Dausch