1tablespoonpure vanilla extract or vanilla bean paste
2ouncesplain Greek yogurt or sour cream
2tablespoonsall-purpose flour
Oreo Layer
12roughly chopped Oreo cookies (about 2/3 of a 14.3 ounce package)
12crushed Oreo cookies
3halved Oreo cookieshalved, for the top
Instructions
PREHEAT AND LINE THE PAN: Heat the oven to 325 degrees F with a rack in the center position. Line a 9x9 inch baking pan with parchment paper, leaving a 2 inch overhang on two opposite sides. Press the parchment flat into the corners so it stays down instead of floating up into the batter. Those two flaps are your handles later, and they are the difference between lifting the bars out whole and digging them out in pieces.
MELT THE BUTTER AND CHOCOLATE: Combine 1 stick (1/2 cup unsalted butter) and 6 ounces semi-sweet chocolate chips in a microwave-safe bowl. Microwave in 20 to 30 second bursts, stirring after each one, until the mixture is glossy and completely smooth with no lumps of chocolate left, about 90 seconds total. Stirring between bursts is what keeps the chocolate from scorching, because the bowl holds heat longer than the chocolate can take.
BUILD THE BROWNIE BATTER: Whisk 3/4 cup granulated sugar and 1/4 cup packed light brown sugar into the warm chocolate until the mixture looks grainy and dull. Add 2 large eggs and stir hard for about a minute, until the batter turns glossy and thick and falls off the spoon in a ribbon. Stir in 1 tablespoon pure vanilla extract or vanilla bean paste. That hard stirring after the eggs go in is what gives brownies their shiny, papery top crust, so the arm work pays off.
FOLD IN THE DRY INGREDIENTS: Add 3/4 cup all-purpose flour, 1/4 cup unsweetened cocoa powder, and 1/2 teaspoon kosher salt. Fold just until no streaks of flour or cocoa are visible, then stop. Folding by hand keeps these fudgy, since extra mixing develops the flour and pushes them toward cakey.
LAYER THE BATTER AND CHOPPED OREOS: Pour about two-thirds of the brownie batter into the lined pan and spread it into an even layer that reaches all four corners, roughly 1/2 inch deep. Scatter 12 roughly chopped Oreo cookies across the surface, leaving them sitting on top rather than pressing them down so they stay in distinct chunks. Set the remaining third of the batter aside at room temperature so it stays soft enough to dollop later.
BEAT THE CREAM CHEESE AND SUGAR: Beat 16 ounces full-fat cream cheese, softened and 1/2 cup granulated sugar until completely smooth with no lumps, about 2 minutes. The cream cheese should be soft enough that your finger leaves a dent easily. Cream cheese straight from the refrigerator stays lumpy no matter how long you beat it, and those lumps bake right in.
FINISH THE CHEESECAKE BATTER: Keep the mixer on low from here. Add 2 large eggs, room temperature and mix just until they disappear, about 30 seconds. Add 1 tablespoon pure vanilla extract or vanilla bean paste, 2 ounces plain Greek yogurt or sour cream, and 2 tablespoons all-purpose flour, and mix until smooth, about 30 seconds more. The batter should look like thick pancake batter and fall from the spatula in a slow ribbon. Fold in 12 crushed Oreo cookies by hand until the batter turns pale gray with dark flecks running through it. Low speed is what keeps this layer flat, because beating air into it makes it puff in the oven and crack as it cools.
POUR THE CHEESECAKE LAYER: Pour the cheesecake batter over the brownie base and spread it gently to the edges. Move slowly so the chopped Oreo pieces stay settled in the brownie layer underneath.
SWIRL AND TOP: Drop the reserved brownie batter over the cheesecake in spoonfuls, spacing them in a rough checkerboard. Drag a butter knife or skewer through the dollops in long S-shaped passes, four or five strokes total, and stop while you can still see distinct dark and pale areas. Press 3 halved Oreo cookies into the surface at even intervals, cut side up, level with the batter. A few passes give you ribbons, and a dozen turns the whole top muddy brown.
BAKE: Bake 40 to 45 minutes, until the edges look set and lightly puffed and the center jiggles as one soft unit when you nudge the pan, like set gelatin rather than liquid. The jiggle is your reliable signal here. If you check with a toothpick it will come out coated with cheesecake batter even when the bars are done, so trust the pan over the pick. Pull the pan while the center still has that gentle jiggle, because the bars keep firming as they cool.
COOL, CHILL, THEN SLICE: Set the pan on a wire rack and cool all the way to room temperature, about 2 hours, until the pan feels cool to the touch. Cover and refrigerate at least 2 hours, or overnight. Lift the slab out using the parchment handles, set it on a cutting board, and cut into 16 squares with a large knife warmed under hot water and wiped dry between every single cut. Cooling on the counter first is what keeps the cheesecake layer smooth, and a warm blade is what leaves clean edges instead of dragged crumbs.
Notes
MAKE-AHEAD: These are better on day two. Bake them a full day ahead, chill overnight, and slice them cold. The extra time firms the cheesecake layer, deepens the chocolate, and gives you sharper edges on every square.STORAGE: Store the bars in an airtight container in the refrigerator. They stay at peak quality for about 3 days, when the brownie layer is still fudgy and the cheesecake is still creamy. They are safe to eat for up to 5 days.FREEZING: Freeze the cut bars in a single layer on a sheet pan until solid, then stack them in an airtight container with parchment between the layers for up to 3 months. Thaw overnight in the refrigerator. Freezing them solid first is what keeps the swirled tops from smudging against each other.INGREDIENT TIP: Use full-fat block cream cheese, not the whipped or spreadable kind sold in tubs. Tub cream cheese carries extra water and air, which loosens the cheesecake layer and can leave it wet in the center.