1. Preheat the Oven: Set your oven to 350 degrees F (175 degrees C). Line a baking sheet with parchment paper.

2. Make the Brownie Batter: In a bowl, whisk together the flour, cocoa powder, baking powder, and salt. In another bowl, blend the melted butter with the granulated sugar until well combined. Beat in the eggs and vanilla extract until smooth. Gradually mix in the dry ingredients until just combined. Fold in the chocolate chips.

3. Prepare the Cheesecake Filling: In a separate bowl, beat the cream cheese with powdered sugar and lemon zest until creamy and smooth.

4. Assemble the Cookie Bites: Pour about 2/3 of the brownie batter into the prepared baking pan, spreading it evenly to cover the base. Drop spoonfuls of the cheesecake filling over the brownie layer, spreading gently to form a thin layer. Drizzle or dollop the remaining brownie batter over the cheesecake layer, then use a knife or toothpick to swirl the two layers slightly for a marbled effect.

5. Bake: Bake in the preheated oven for 20-25 minutes, or until the edges are set but the center is still slightly soft. Remove from the oven and allow the tray to cool completely on a wire rack.

6. Cut into Bites: Once fully cooled, lift the baked mixture out of the tray using the parchment overhang. Place it on a cutting board and cut into small bite-sized squares or rectangles.