Whisk melted butter, sugar, eggs, and vanilla. Stir in flour, cocoa, salt, and chocolate chips until just combined.

Spread the brownie batter in a lined square pan and bake until the edges are set and the center has moist crumbs. Cool briefly.

Beat softened cream cheese with powdered sugar, egg, vanilla, and peppermint. Spread over the warm brownie layer.

Bake until the cheesecake is gently set. Cool, chill thoroughly, drizzle with white chocolate, and sprinkle with crushed candy cane.