Oven Preparation: Initiate the heating process of the oven to a temperature of 350º F. Prepare an 8×8 or 9×9 inch baking pan by lining it with either aluminum foil or parchment paper. Ensure it is lightly coated with non-stick cooking spray to prevent adherence.

Flour Mixture Preparation: In a suitably sized mixing vessel, amalgamate the all-purpose flour, salt, and cocoa powder. Ensure thorough mixing. Set aside for later incorporation.

Chocolate Mixture Preparation: Using a small saucepan, place it over low heat. Introduce the finely chopped unsweetened chocolate and cubed butter to the saucepan. Periodically stir the contents until a uniform melted mixture is achieved. This should take approximately 5 minutes.

Wet Mixture Preparation: In a separate, larger mixing vessel, introduce the granulated sugar, whole eggs, and additional egg yolk. Utilize an electric mixer to blend the contents for a duration of 1 minute or until the mixture adopts a pale yellow hue and has doubled in volume.

Combining Mixtures: Carefully introduce the previously prepared chocolate mixture into the wet mixture. Subsequently, add the vegetable oil and pure vanilla extract. Incorporate the flour mixture gradually, ensuring that it is mixed until just combined.

Pan Preparation: Reserve approximately 1/3 cup of the final batter. Transfer the remaining batter to the prepared baking pan and level it out. Set aside.

Cream Cheese Mixture Preparation: In a clean mixing vessel, combine the room temperature cream cheese, granulated sugar, and whole egg. Use an electric mixer to achieve a smooth consistency over a duration of 1-2 minutes. Transfer this mixture to a piping bag or an alternative such as a ziplock bag with a corner excised.

Swirling Process: Execute a grid pattern atop the batter in the baking pan using the cream cheese mixture from the piping bag. With a butter knife or a similar utensil, create swirls by dragging it across the grid pattern. Introduce the previously reserved 1/3 cup of batter to fill any gaps and execute additional swirling.

Baking Procedure: The baking duration is contingent upon the type of baking pan in use. If utilizing a glass pan, bake for 35-38 minutes. If a metal pan is in use, bake for 30-35 minutes. The brownies are considered done when a toothpick or probe, upon insertion, emerges clean. For a less fudgy consistency, extend the baking duration as mentioned in the original recipe.

Cooling Phase: Post baking, it is imperative to allow the brownies to return to room temperature prior to slicing.