Preheat your oven to 350°F (175°C). Line a 9×13-inch baking pan with parchment paper, leaving some overhang on the long sides for easy lifting. Lightly grease the parchment with butter or non-stick spray.
In a large microwave-safe bowl, melt the butter in 20–30 second bursts until fully melted but not sizzling. Let it cool until warm, not hot. Whisk in the granulated sugar and light brown sugar until the mixture looks thick and glossy.
1 cup unsalted butter, 2 cups granulated sugar, 1/2 cup light brown sugar
Add the eggs one at a time, whisking well after each addition, then whisk in the vanilla. The mixture should look very shiny and slightly thick; this helps create a crackly brownie top.
4 large eggs, 2 teaspoons pure vanilla extract
In a separate medium bowl, whisk together the cocoa powder, flour, salt, and baking powder.
1 cup unsweetened cocoa powder, 1 cup all-purpose flour, 1/2 teaspoon fine sea salt or table salt, 1/2 teaspoon baking powder
Gently stir the dry ingredients into the wet mixture using a spatula or wooden spoon, mixing just until no dry streaks remain. If using, fold in the chocolate chips or chopped chocolate. The batter will be thick.
1 cup unsweetened cocoa powder, 1 cup all-purpose flour, 1/2 teaspoon fine sea salt or table salt, 1/2 teaspoon baking powder, 1 cup semi-sweet chocolate chips or chopped chocolate
In another medium bowl, beat the softened cream cheese until completely smooth and no lumps remain. Add the sugar, egg yolk, vanilla, and sour cream or Greek yogurt (if using), then beat again until creamy and slightly fluffy. The mixture should be smooth and spreadable.
8 oz cream cheese, 1/3 cup granulated sugar, 1 large egg yolk, 1 teaspoon pure vanilla extract, 1–2 tablespoons sour cream or plain Greek yogurt
Spread about 3/4 of the brownie batter evenly into the prepared pan, smoothing it into the corners. Dollop the cream cheese mixture over the top in 8–10 large spoonfuls. Spoon the remaining brownie batter in between and around the cream cheese dollops.
Using a butter knife or skewer, gently swirl the cream cheese mixture and brownie batter together with slow figure-eight motions. Make 4–6 passes across the pan; do not over-swirl, so you keep distinct streaks of white and dark batter.
Bake in the preheated oven for 32–40 minutes. Start checking around 30 minutes. Insert a toothpick into the brownie portion (not a cream cheese pocket); it should come out with a few moist crumbs but no wet batter. The cream cheese areas should look set and no longer shiny, and the edges will be slightly puffed.
Place the pan on a cooling rack and let the brownies cool completely in the pan, about 1–2 hours. For the cleanest slices and best texture, chill the cooled brownies in the refrigerator for at least 1 hour before cutting into squares.