Preheat oven to 350F. Line a 9x13-inch baking pan with parchment paper, leaving an overhang on two sides for easy removal. Lightly grease the parchment.

In a large bowl, whisk melted butter and sugar until well combined, about 1 minute. Add eggs one at a time, beating well after each addition, then stir in vanilla. Fold in cocoa powder, flour, and salt until just combined and no dry streaks remain. Do not overmix.

In a medium bowl, beat pudding mix and cold milk with an electric mixer on medium speed for 2 minutes until thickened and smooth. It will be looser than typical pudding, which is correct for swirling.

Spread two-thirds of the brownie batter evenly in the prepared pan. Dollop half the pudding over the batter in large spoonfuls. Add remaining brownie batter in dollops, then top with remaining pudding. Use a knife or skewer to swirl the layers together in figure-eight motions, creating a marbled pattern. Do not over-swirl or the colors will muddy.

Sprinkle half the crushed vanilla wafers evenly over the top, pressing gently so they adhere.

Bake 32-36 minutes until the edges are set and a toothpick inserted in the center comes out with moist crumbs but no wet batter. The center should look slightly underdone; it will firm up as it cools. Do not overbake.

Cool completely in the pan on a wire rack, at least 2 hours. Lift out using parchment overhang, cut into squares, and sprinkle with remaining crushed vanilla wafers just before serving.