Preheat the oven to 375℉. Line a 15" x 10" jelly roll pan with parchment paper, or lightly spray with nonstick cooking spray and lightly flour.
Beat eggs in a large bowl or electric mixer until thick. Gradually beat in the sugar. Add water and pumpkin purée.
Whisk or sift flour, baking powder, pumpkin pie spice, cinnamon, nutmeg, and salt together in a bowl. Slowly add dry ingredients to the bowl of wet ingredients. Mix well.
Pour the pumpkin mixture into the prepared jelly roll pan.
Bake in the oven for 12-15 minutes. As soon as it sets, remove from the oven. Lightly touch the top of the pumpkin roll, and if it springs back, it's done.
Lay a thin towel or cheesecloth down and lightly sprinkle it with confectioners' sugar. While it's still warm, carefully flip the pumpkin roll onto the towel. Remove the parchment paper. Roll the short end of the pumpkin roll with the towel. Allow it to cool while rolled for about 30 minutes.
Filling
In a large bowl with a hand mixer or an electric mixer, beat cream cheese and sugar on medium speed until fluffy. Fold in Cool Whip with a spatula until well blended.
Carefully unfold the pumpkin roll after it's cooled. Spread the cream cheese filling to the edges of the pumpkin roll. Roll the pumpkin roll back up and cover with plastic wrap. Place in the refrigerator to chill for at least 1 hour before slicing and serving.