Preheat oven to 350 degrees F. Line a 15x10 inch pan with non-stick foil or just spray with cooking spray.
Pumpkin Batter: Beat the melted butter, salt (if using) and sugar until smooth. Beat in the eggs, pumpkin, and water until well blended, scraping down sides of bowl as needed.
Mix flour, baking soda, baking powder, cinnamon and nutmeg together in a separate bowl; stir into batter.
Spread all but a few tablespoons batter evenly in prepared pan. Reserve the few tablespoons of batter
Swirl: In a second bowl, beat cream cheese, sugar and vanilla until smooth. Add egg and beat just until it’s mixed in. Drop tablespoons of cheese mixture over pumpkin batter, then drag a knife through to make marbles. Drop reserved tablespoons of pumpkin batter over top. The reason for this is, there’s a lot of white batter, so putting a few tablespoons of pumpkin batter on top gives more of a contrast.
Bake on center rack until pumpkin batter springs back when touched, about 30 minutes. Let cool completely in pan, then chill for an hour or more. Cut into 24 bars.