In a large bowl, whisk together melted butter, sugar, and vanilla.
Add the eggs, one at a time, whisking well after each addition.
Stir in the cocoa powder, flour, and salt, mixing until just blended.
Spread the brownie batter evenly over the crust.
Place the cookie butter in a small heatproof bowl. Heat for 20-30 seconds, or until melted and thinned. Heat at additional 10 second intervals as needed.
Drizzle the melted cookie butter over the brownie batter, and lightly swirl with a knife.
Bake at 350 degrees for 40-45 minutes, or until edges and center appear set, and a toothpick inserted near the center comes out mostly clean, with only a few moist crumbs.
Cool in the pan on a wire rack.
Once completely cool, run a knife around any exposed edges. Carefully lift the brownies out by the foil overhang.
Transfer to a plate or serving platter.