Heat the oven to 350 degrees and line a baking sheet with parchment paper.
In a mixing bowl, cream the softened butter and granulated sugar until light. Add the egg and vanilla extract, then mix until smooth.
Stir in the flour, baking powder, and salt until a soft dough forms.
Roll the dough into 8 small balls, place them on the baking sheet, and flatten each slightly with your palm.
Bake for 10 to 12 minutes until the edges turn light golden. Let the cookies cool completely on the sheet.
In a small bowl, whisk the powdered sugar and milk until the glaze reaches a spreadable consistency.
Spread the white glaze over each cooled cookie and let it set for a few minutes.
Melt the dark chocolate chips in a microwave-safe bowl in 20-second bursts, stirring between each. Spoon the melted chocolate into a small piping bag or zip-top bag with one corner snipped.
Pipe three or four thin concentric circles on each cookie, then drag a toothpick from the center outward to form the web pattern. Let the chocolate set before serving.