6 tablespoons unsalted butter, melted and cooled, plus more for greasing the pan
1 3/4 cups (12 1/4 ounces) granulated sugar, divided
3 large eggs, divided
1 cup canned pumpkin puree
1 3/4 cups (8 3/4 ounces) all-purpose flour
1/2 teaspoon kosher salt
1 1/2 teaspoons ground cinnamon
1 teaspoon baking soda
1/2 teaspoon baking powder
1/2 teaspoon ground nutmeg
1 package (8 ounces) cream cheese, at room temperature
Preheat the oven to 350°F. Butter and flour a 13-by-9-inch casserole dish.
In a large mixing bowl, whisk together the butter and 1 1/2 cups sugar until smooth. Whisk in 2 eggs, pumpkin, and 1/3 cup water until well blended. In another mixing bowl, whisk together the flour, salt, cinnamon, baking soda, baking powder, and nutmeg. Fold into the butter mixture until no streaks of flour remain. Spread batter evenly in the prepared casserole dish.
In a bowl, with an electric mixer on medium speed, beat cream cheese, remaining egg, and remaining 1/4 cup sugar until smooth.
Drop cream cheese mixture in evenly spaced 1-tablespoon dollops over the batter. Use a butter knife to swirl the batter, gently folding some of the cream cheese mixture under the pumpkin batter.
Bake until the center of pumpkin batter (not the cream cheese mixture) springs back when touched, about 30 to 32 minutes. Let cool completely in pan, and then cut into 20 bars.