To make the cookies, in a medium bowl, whisk together flour, baking powder and salt; set aside.

In a large bowl, using an electric mixer fitted with the paddle attachment, beat together butter and granulated sugar on medium speed until light and fluffy, about 3 minutes.

Beat in egg and vanilla until well blended.

Add flour mixture and beat on low speed just until combined.

Divide dough in half and shape into 2 disks.

Wrap in parchment or waxed paper and refrigerate until firm, at least 1 hour or overnight.

Preheat oven to 350°F.

Line 2 baking sheets with parchment paper.

Working with one disk of dough at a time on a floured surface, roll out dough 1/4-inch thick and cut out cookies with a floured 3-inch round cookie cutter.

Transfer to the prepared baking sheets, spacing them 1 inch apart. Repeat with remaining dough.

Bake until cookies are just golden around the edges, 10 to 12 minutes.

Transfer cookies to a wire rack and let cool completely.

To make the icing, melt chocolate chips in a microwave or a double boiler and let cool slightly.

Transfer to a piping bag or a resealable plastic bag and set aside.

In a medium bowl, whisk together powdered sugar, milk, corn syrup and vanilla until smooth (mixture will be quite thick but pourable).

Transfer sugar icing to a separate piping bag or a resealable plastic bag.

Cut open tip of piping bag about 1/4 inch wide.

Working with 2 cookies at a time, pipe a circle of sugar icing and fill in with more icing, leaving a 1/2-inch border around edge of cookie (spread until smooth with an offset spatula if needed).

Cut open tip of melted chocolate piping bag about 1/8 inch wide.

Starting in center of cookie, pipe a spiral moving out toward edge of cookie.

Use a toothpick to drag icing from center out toward edge to create a spider web.

Let sit on the wire racks or baking sheet until icing is set. Cookies will keep in an airtight container at room temperature for up to 3 days.