Preheat the oven to 350°F and line an 8x8 baking pan with parchment paper.
Melt the butter in a saucepan over low heat, then remove from heat and stir in the sugar until combined.
Add the eggs and vanilla extract, mixing well after each addition.
Stir in the cocoa powder, flour, and salt until the batter looks smooth.
Fold in the semisweet chocolate chips.
Pour the batter into the prepared pan and spread evenly.
Bake for 25 minutes, then let the brownies cool completely in the pan.
Melt the white chocolate chips in the microwave in 20-second bursts, stirring between each.
Spoon the melted white chocolate into a small zip-top bag, snip a tiny corner, and pipe several circles on top of the cooled brownies.
Drag a toothpick from the center outward through each circle to create the web pattern, then cut into squares.