Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish or line it with parchment paper for easy removal.
In a large mixing bowl, combine the melted butter, granulated sugar, and 1 teaspoon vanilla extract. Mix until well combined. Add the eggs one at a time, mixing well after each addition.
In another bowl, whisk together the flour, cocoa powder, and salt. Gradually add the dry ingredients to the wet mixture, stirring until just combined. Fold in the chopped Milky Way bars.
Pour half of the brownie batter into the prepared baking dish and spread it evenly.
In a separate bowl, beat the softened cream cheese, powdered sugar, and 1 teaspoon vanilla extract until smooth. Spoon the cream cheese mixture over the brownie layer, spreading it gently.
Drizzle the caramel sauce over the cream cheese layer, then pour the remaining brownie batter on top. Use a knife or toothpick to swirl the layers together for a marbled effect.
Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs.
Allow the brownies to cool completely in the pan before cutting into squares.
Serve warm or chilled, drizzling additional caramel sauce over the top for a decadent touch.