Pre-heat oven to 350 degrees and lightly spray a 9x9 pan with cooking spray.
Put cream cheese in the bowl of a stand mixer or in a large bowl with a hand mixer and beat it at medium speed for about 2 minutes, until smooth.
Add granulated sugar and peppermint extract and beat together until well combined. Add the whole egg and the 1 egg white and beat well. Add flour and beat until just combined.
Divide cream cheese batter into two bowls. Leave on bowl as is and stir in a few drops of red food coloring to the other bowl, until mixture reaches the shade of pink or red you desire.
For brownie batter, whisk together flour, cocoa powder, and salt in a medium bowl.
In the bowl of a stand mixer or in a large bowl with a hand mixer, combine brown sugar, oil, buttermilk, vanilla, whole egg, and 2 egg whites and beat until just blended.
Pour brownie batter into prepared pan. Pour white cream cheese mixture on top of the brownie batter, spreading to the edges. Dot the red batter over the top and gently swirl with the white using the tip of a knife.
Bake for 25-27 minutes, until the cheesecake topping is set. Cool in pan on a wire rack before slicing into squares.