Preheat oven to 350 degrees F. Spray a 9 x 13 inch baking pan with non-stick cooking spray.
In a medium bowl, whisk together all-purpose flour, whole-wheat flour, baking powder, baking soda, cinnamon, ginger, nutmeg, cloves and salt. Set aside.
In a larger bowl, whisk the eggs and sugars until combined. Whisk in the pumpkin puree, oil, buttermilk and vanilla. Stir in the dry ingredients until combined. Spread about 2/3 of the batter evenly into the prepared pan. Set aside.
In a bowl, with an electric mixer on medium speed, beat cream cheese, egg, sugar and vanilla until fully incorporated and smooth, scraping down the sides if necessary.
Spread this cream cheese mixture evenly over the pumpkin batter. Dollop the remaining pumpkin batter over the cream cheese layer. Take a butter knife and gently swirl the batter. Sprinkle the walnuts over the top, and using a spatula, gently press into the batter.
Bake for 30-35 minutes, or until the center of the pumpkin batter is set and springs back when touched. Remove from oven and let cool completely in pan on a cooling rack. Cut into squares and serve.
Store these pumpkin roll bars in an airtight container in the refrigerator.