Make the cookies: Whisk the flour, cocoa powder, baking powder and salt in a medium bowl. Beat the butter, shortening and granulated sugar in a large bowl with a mixer on medium-high speed until light and fluffy, about 2 minutes. Add the egg, vanilla and food coloring and beat until smooth and the color is fully incorporated. Reduce the mixer speed to low; add the flour mixture and beat until just combined. Cover and refrigerate until firm, about 1 hour.
Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Line 2 baking sheets with parchment paper. Roll tablespoonfuls of dough into balls and arrange 2 inches apart on the prepared baking sheets. Bake, switching the pans halfway through, until the cookies are puffed and set, 16 to 18 minutes. Let cool 2 minutes on the baking sheets, then make an indentation in each cookie using the back of a small measuring spoon. Transfer to racks to cool completely.
Make the filling: Microwave the white chocolate and heavy cream in a microwave-safe bowl in 20-second intervals, stirring, until smooth. Beat the cream cheese, butter and confectioners' sugar in a bowl with a mixer on medium-high speed until smooth and fluffy, about 2 minutes. Add the white chocolate mixture, vanilla and salt and beat until smooth. Transfer to a pastry bag fitted with a star tip and pipe into the indentations in the cookies. Sprinkle with red sanding sugar. Store in the refrigerator.