Preheat oven to 325°. Spray an 8-inch square pan with vegetable cooking spray.
Beat cream cheese, 2 Tbsp. sugar, and 1/2 tsp. vanilla with an electric mixer until creamy and smooth. Add yolk to cream cheese mixture. Stir to combine.
Whisk together flour, cocoa, baking powder, and salt in a small bowl.
Heat oil and chocolate in a medium saucepan over medium heat, whisking until chocolate is melted. Whisk in remaining 1 cup sugar, and stir until melted. Add buttermilk, applesauce, and remaining 2 tsp. vanilla. Remove from heat. Add egg white and whole egg, whisking constantly until incorporated to prevent eggs from curdling. Add flour mixture, stirring until just combined. Transfer brownie batter to prepared pan.
Using a tablespoon, drop 9 dollops of cream cheese mixture on brownie batter. Draw the tip of a sharp knife or skewer through the 2 batters in a crisscross fashion to create a swirled effect.
Bake at 325° for 40 minutes or until top is just firm to the touch, rotating halfway through baking. Cool completely in pan on a wire rack (about 1 hour).
Coat a knife with vegetable cooking spray, and cut into 16 squares. Refrigerate in an airtight container up to 3 days.