Preheat oven to 425 degrees F. Lightly coat an 8- by 8-inch baking pan with cooking spray.
In a medium bowl, whisk together the pumpkin puree, cream cheese, 1 egg, maple syrup, ginger, nutmeg and salt until combined.
Pour the pumpkin mixture into the prepared baking pan. Bake until the mixture is just set, 7 to 9 minutes. Let cool for 5 minutes.
Line a baking sheet with parchment paper and lightly coat it with cooking spray.
Whisk the remaining egg and water in a small bowl to make an egg wash.
Working with one egg roll wrapper at a time, lay the wrapper on a cutting board and brush the egg wash around each edge.
Scoop 2 tablespoons of the cooked pumpkin mixture onto one edge of the wrapper, leaving a small border. Sprinkle 2 teaspoons of the crushed gingersnaps over the pumpkin filling.
Fold in the sides and roll up the egg roll tightly. Place it on the prepared baking sheet.
Repeat with the remaining wrappers, pumpkin filling and gingersnaps.
Bake until the egg rolls are light golden brown, 15 to 20 minutes. Remove from the oven and brush each egg roll with the egg wash, then sprinkle with cinnamon. Return to the oven and bake for 5 minutes.
Serve hot with dairy-free whipped topping, if desired.