Preheat oven to 325 degrees F (165 degrees C). Spray a 9x13-inch baking dish with cooking spray.
Place flour, confectioners' sugar, and salt in a food processor; pulse until blended. Add cold butter pieces and vanilla extract; blend until mixture forms clumps. Press butter-flour mixture evenly into the prepared baking dish.
Bake in the preheated oven until lightly browned, about 10 minutes. Pierce dough all over with a fork while still hot. Slice dough into 12 squares, then cut each square in half diagonally, forming 24 triangle cookies.
Return cookies to the oven and continue to bake until golden brown, 30 to 35 minutes more. Trace a knife around each cookie to ensure they're completely sliced. Cool in the pans for 10 minutes before removing to cool completely on a wire rack.
Melt white chocolate in a microwave-safe bowl in 30-second intervals, stirring after each melting, for 1 to 3 minutes (depending on your microwave). Drizzle white chocolate over cookies in a zigzag pattern, using a fork.
Melt milk chocolate chips, 2 tablespoons butter, and corn syrup in another microwave-safe bowl in 30-second intervals, stirring after each melting, for 1 to 3 minutes. Drizzle milk chocolate mixture over white chocolate, using a clean fork. Sprinkle almonds over chocolate. Let stand until chocolate sets, about 1 hour.