Preheat your oven to 350°F (175°C). Lightly grease a 13x9-inch baking pan or line it with parchment paper for easier removal.

In a large mixing bowl, combine the brownie mix, water, oil, and eggs according to the package instructions. Stir until smooth and well blended. Pour the batter into the prepared pan, spreading evenly.

In a separate medium bowl, beat the softened cream cheese using an electric mixer on medium speed until smooth. Add the granulated sugar and continue mixing until fully incorporated. Then add the egg and vanilla extract, mixing until the topping is uniform and creamy.

Spoon the cream cheese mixture in small dollops across the surface of the brownie batter. Using a knife or skewer, gently swirl the two mixtures together to create a marbled effect. Avoid over-mixing to preserve the distinct swirls.

Bake in the preheated oven for 35 to 40 minutes, or until the center is set and a toothpick inserted near the center comes out with a few moist crumbs. Remove from the oven and allow to cool completely in the pan on a wire rack.

Once cooled, cut the brownies into squares and serve. Store any leftovers in an airtight container in the refrigerator for up to 5 days. These brownies may also be frozen for longer storage.