Heat oven to 350º F. Spray a 13x9-inch baking pan with non-stick cooking spray. Set aside.
In a large bowl, with mixer on medium speed, beat together butter and sugar until smooth.
Add eggs, pumpkin puree, 1 teaspoon of vanilla extract/paste, and water. Mix until well blended.
In a small bowl, whisk together flour, cinnamon, cloves, ginger, nutmeg, baking soda, baking powder, and salt. Add the dry ingredients to the pumpkin mixture and blend until well combined.
For the cream cheese mixture, in a small bow, beat together cream cheese, egg, sugar, and vanilla extract/paste until smooth.
Spread 2/3 of the pumpkin batter into the prepared baking pan. Spread all of the cream cheese mixture over the pumpkin batter. Dollop the remaining pumpkin cake batter over the cream cheese mixture and spread as evenly as possible.
Using the handle of a butter knife, swirl together the top layer of pumpkin batter and cream cheese mixture.
Bake 30 to 35 minutes or until the center of the pumpkin bars spring back when touched. Cool completely in pan before cutting and serving.