Preheat your oven to 350°F (175°C). Line a 9x13-inch baking pan with parchment paper or grease it lightly to prevent sticking.
In a large mixing bowl, cream together 1 cup softened unsalted butter and 2 cups granulated sugar until smooth and fluffy. Beat in the 4 large eggs, one at a time, followed by 1 tablespoon vanilla extract.
In a separate bowl, sift together 1 cup all-purpose flour, 1/2 cup unsweetened cocoa powder, and 1/4 teaspoon salt. Gradually add the dry ingredients to the wet mixture, stirring just until combined. Be careful not to overmix.
In another bowl, beat together 1 cup softened cream cheese and 1/2 cup powdered sugar until smooth and creamy. Add 1/4 cup milk and mix well to create a pourable cheesecake batter.
Pour half of the brownie batter into your prepared pan, spreading it evenly. Drop spoonfuls of the cheesecake batter over the brownie layer, then gently swirl it with a knife or skewer to create a marbled effect. Sprinkle half of the chopped Milky Way candy bars and 1/4 cup chocolate chips over the swirled layer.
Spread the remaining brownie batter over the swirled cheesecake layer. Top with the rest of the chopped Milky Way bars and chocolate chips, pressing them slightly into the batter.
Bake in the preheated oven for 35 to 40 minutes, or until a toothpick inserted into the center comes out with just a few moist crumbs. The cheesecake swirls will be set but still creamy.
Allow the Milky Way cheesecake brownies to cool completely in the pan on a wire rack. Once cooled, lift them out using the parchment paper edges and cut into squares to serve.