Preheat the oven to 350 degrees and line a baking sheet with parchment paper.
Whisk together the flour, cocoa powder, baking soda, and salt in a medium bowl.
In a separate bowl, beat the softened butter and sugar until light and fluffy. Add the egg and mix until combined.
Stir the dry ingredients into the wet mixture until a dough forms. Fold in the semisweet chocolate chips.
Scoop rounded tablespoons of dough onto the prepared baking sheet, spacing them a few inches apart. Bake for 8 to 10 minutes until the edges are set.
Let the cookies cool on the sheet for 5 minutes, then transfer to a wire rack to cool completely.
Melt the white chocolate chips in a microwave-safe bowl in 20-second bursts, stirring between each until smooth. Spoon into a piping bag or zip-top bag with a small corner snipped off.
Pipe circles on each cooled cookie, then draw lines from the center outward to create a spiderweb pattern.