Preheat oven to 350 degrees F. Grease and line the bottom of an 8x8-inch baking pan with parchment paper.
In a medium-sized bowl whisk together, the cocoa powder, ¾ cup flour, salt and set aside.
Separate the white and yolk from one egg and place them each in a small bowl and set aside
Heat butter in a large microwave-safe bowl, add the chocolate chips. Let it sit until the chocolate has softened (about 3 to 4 minutes). Stir until smooth.
Add the brown sugar, stirring until incorporated into the chocolate mixture.
Add the vanilla and 2 eggs and the yolk of the third egg, and stir until well combined.
Add the flour mixture to the big bowl of the chocolate mixture and stir with a soft silicone spatula until the brownie batter is well combined.
Place 1 cup of the batter in a small bowl, mix in 2 tablespoons of water and set aside.
Transfer the big bowl of brownie batter to the prepared baking pan using an offset spatula or soft silicone spatula to smooth the batter (the batter will be thick). Set aside while making the cream cheese topping.
In a large bowl with a handheld mixer, beat the cream cheese until light and fluffy, slowly add in the granulated sugar and continue beating. Add the egg white and continue to beat until smooth. Sprinkle in the 1 tablespoon of flour and stir until well combined.
Using a small cookie scoop or tablespoon, dollop the cream cheese mixture over the brownie batter, spacing them evenly in the baking pan. Repeat with the reserved chocolate batter mixture, filling in the spaces between the cream cheese dollops.
Using the tip of a knife, gently swirl the top ¼-inch layer of the cream cheese & chocolate batter mixture together.
Place the baking pan on the center rack in the oven and bake for 25 to 30 minutes until the edges are baked but the center is soft but doesn’t jiggle when shaken.
Remove from oven and place on a wire rack to cool for 2 hours before cutting.