Heat oven to 350. Mix flour, baking powder and salt together in a medium bowl. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream butter and sugar on medium-high speed, till thoroughly mixed, about 2-3 minutes. Add the egg and vanilla and beat on medium speed, scraping the sides of the bowl with a spatula as needed.
Gently add the dry ingredients and beat on low speed until just combined, making sure to scrape bowl as needed so that everything gets well combined.
Separate dough into 2 balls and wrap in plastic wrap. Flatten out into a somewhat imperfect disc, so that it will chill quicker. Refrigerate for about 30 minutes till firm.
Remove 1 disc of dough at a time and unwrap. With a rolling pin, roll out dough to about ¼-inch thickness on a floured work surface.
To make the spider web designs, simply cut out round circles using a glass or round cookie cutter.
Set cookie cutouts on a cookie sheet lined with parchment paper or a silicone mat. Make sure to leave about 1.5″ space between cookies as they will expand. Bake for 12-14 minutes at 350 degrees f, till cookies are light golden brown.
Allow to cool on a wire rack before icing. If cookies are too warm when iced, the icing will run all over and not harden.