Preheat the oven to 325 F. Line 8 x 8 inches pan with parchment paper leaving large overhand the sides, then and spray with cooking spray, set aside.
In a large, microwave-safe bowl combine white chocolate and butter, microwave for 30-second increments, stirring between each until melted.
Cool for 5 minutes, then whisk in sugar. Add eggs, lemon zest, salt, and lemon extract and whisk until evenly combined.
Finally, fold in the flour. Reserve ½ cup of mixture for topping and spread the remaining mixture in prepared pan.
Beat cream cheese with sugar and vanilla until smooth. Mix in egg just to combine. Spoon cream cheese mixture over lemon mixture and gently smooth the top.
Drop small spoonfuls of reserved brownie batter on top of the cheesecake layer. Using a toothpick or a thin knife, swirl the batter.
Bake for 30-35 minutes in the preheated oven or until the center looks set and a toothpick inserted in the center comes out clean or with just a few damp crumbs.
Cool completely, then cover and refrigerate for at least 4 hours or overnight. Chilling the brownies in the fridge allows them to fully set and ensures that the brownies cut beautifully with clean edges. Also, chilling in the fridge actually improves the flavor, too.
When ready to serve remove from the fridge and lift the brownies out of the pan using the overhang from parchment paper. Cut into squares using a sharp knife.
