Preheat the oven to 350 degrees F and line a small 6x6 inch baking pan with parchment paper.
Melt the butter in a microwave-safe bowl, then stir in the granulated sugar until combined.
Add the egg and 1/2 teaspoon of the vanilla extract, and mix until smooth.
Stir in the cocoa powder, flour, and salt until no dry streaks remain.
Spread the batter evenly in the prepared pan and bake for 18 to 20 minutes, until a toothpick comes out with a few moist crumbs.
Let the brownies cool completely in the pan.
In a small bowl, whisk the powdered sugar, milk, and remaining 1/2 teaspoon vanilla extract until smooth and pourable.
Transfer the icing to a zip-top bag, snip a tiny corner, and pipe four concentric circles on top of the cooled brownies.
Drag a toothpick from the center outward through the circles to create the web design, then slice into four squares.