1. Preheat the oven to 350°F (175°C) and line an 8×8-inch baking pan with parchment paper. Lightly grease the paper for easy removal.

2. Melt the butter and allow it to cool slightly before mixing.

3. In a large bowl, whisk together the melted butter and granulated sugar until smooth.

4. Add the eggs one at a time, mixing well after each addition.

5. Stir in the vanilla extract, buttermilk, and red food coloring until fully combined.

6. Add the cocoa powder, flour, and salt. Mix gently until no dry streaks remain.

7. In a separate bowl, beat the softened cream cheese until smooth.

8. Add the powdered sugar, vanilla extract, and lemon juice to the cream cheese mixture and beat until creamy.

9. Spread most of the red velvet brownie batter into the prepared pan, reserving a few spoonfuls for the swirl topping.

10. Carefully spread the cheesecake mixture over the brownie layer.

11. Spoon the reserved brownie batter over the cheesecake layer.

12. Use a knife or skewer to gently swirl the layers together without overmixing.

13. Bake for 30 to 35 minutes or until the edges are set and the center is slightly soft.

14. Allow the brownies to cool completely before slicing for clean squares.

15. Slice and serve chilled or at room temperature.