Place flour, cocoa powder and baking powder in a medium and whisk to combine.
In a large bowl, cream butter, sugar and salt with a handheld mixer until light and fluffy. Alternatively, use a stand mixer fitted with a paddle attachment. Mix in egg and vanilla, scraping down bowl as needed. Add dry ingredients and mix until just combined. Turn out the dough to a lightly floured surface and divide in half. Shape into two disks, wrap in plastic wrap and chill at least 1 hour.
Preheat oven to 350°F. Line 2 baking sheets with parchment paper and set aside.
Place one disk of dough between two sheets of parchment paper and roll out to a ¼-inch thick. Repeat with remaining piece of dough. Cut out rounds with a 2-inch cookie cutter and transfer to prepared baking sheet. Use a smaller round to cut the centers out of half the cookies. Re-roll and chill scraps as needed. Place unbaked cookies in the freezer for 10 minutes.
Bake for 10-12 minutes, or until cookies are set on the edges. Let cool on the baking sheet.
Use prepared white icing to decorate half of the cookies with spider webs. These will be the tops. Let icing harden. To assemble, spread a teaspoon of caramel sauce on a full cookie and top with a decorated spider web cookie. Store in an airtight container for up to 3 days.