Cream the butter and sugar. Add the egg and beat until fluffy. Blend in the vanilla. Sift in the flour, baking powder, and salt, mixing until just combined. Wrap the dough in plastic wrap and chill for 1 hour.
Preheat the oven to 350 degrees. On a floured surface, roll half of the dough to 1/8-inch thick. Cut into circles using a 3-inch round cookie cutter or the top of a drinking glass. Gather and reroll scraps. Repeat with remaining dough. Place the cookies on a greased baking sheet and bake for about 8 minutes, until just golden. Do not allow cookies to brown.
To decorate, melt the chocolate chips in the microwave in a heatproof bowl for 1 minutes. The chips may look unmelted, but stir them with a spoon to see if they have actually softened before putting them in for another minute, if necessary. Spoon the melted chocolate into a zipper-lock bag. Seal the bag, pressing out any air. Use a toothpick to make a very tiny hole in one corner of the bag to release a very thin stream of chocolate for writing.
To make the spiderwebs, spread white royal icing smoothly over the surface. Immediately, before the icing can set, pipe a spiral of chocolate over the surface, starting in the middle and working outward. Starting in the center, use a toothpick to pull outward through the icing, making a spiderweb design.
With beaters or a standing mixer, whip the egg white and lemon juice until frothy. At medium speed, beat in the confectioners' sugar, a little at a time, until the mixture is thick but still liquid enough to beat. Then beat on high until the mixture is thick and glossy, about 3 minutes. Cover the surface with plastic wrap while waiting to use it. Royal icing will set to a firm, glossy finish when applied to a cookie. The icing can be stored, tightly covered, in the refrigerator for up to a week.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.