Line a 9x9-inch baking pan with a parchment paper and grease the baking pan. Set aside.
Place softened butter and chopped chocolate in a large heat-resistant bowl, and melt them in a water bath, stirring together until smooth.
Remove the bowl with the melted chocolate from the heat and stir in the salt and vanilla extract.
Mix the white and brown sugars into the melted chocolate, then add in the cocoa powder and the eggs; whisk well until mixture is incorporated and smooth.
Gradually stir in the all-purpose flour and mix until well combined by using a spatula or wooden spoon.
Pour the brownie batter into the prepared pan and smooth it into an even layer. Set aside.
In a medium mixing bowl, beat the cream cheese, granulated sugar, egg, and vanilla extract until smooth. Drop spoonfuls of the cream cheese mixture over the brownie batter. Use a skewer or knife to swirl the cream cheese mixture into the brownie batter.
Sprinkle the chocolate chips over the top of the brownies.
Bake the brownies for 30 to 35 minutes, or until a toothpick inserted into the center comes out clean.
Remove the brownies from the oven and let them cool in the pan for 10 minutes before slicing and serving.
Notes
Use good quality chocolate: Choose chocolate with high cocoa content for the best flavor.
Use quality cocoa powder: Cocoa powder will give the brownies a rich chocolate flavor and a fudgy texture.
Don't overmix the batter: Overmixing the batter can result in cakey brownies. Mix the batter just until the ingredients are combined.
Don't overbake the brownies: Brownies should be removed from the oven when they are just set in the center. A toothpick or cake tester inserted into the center should come out with a few moist crumbs clinging to it.
Let the brownies cool completely before cutting: This will help the brownies to set and cut neatly.
Add-ins: Add a tablespoon or two of brewed coffee or brewed espresso to enhance the chocolate flavor. Also, try adding chopped nuts, jam, chocolate chips, or a swirl of peanut butter to the batter for added flavor and texture.
Butter: You will need to use 2/3-cup softened unsalted butter. That's about 10.5 tablespoons or 151 grams.