Preheat the oven to 350°F (175°C).
In a large mixing bowl, combine the pumpkin puree, peanut butter, coconut oil, and egg (if using).
Gradually add the rolled oats and mix until well combined.
If the mixture is too dry, add water one tablespoon at a time until the desired consistency is achieved.
Roll out the dough on a floured surface to about 1/4 inch thick.
Cut into sticks or desired shapes and place them on a parchment-lined baking sheet.
Bake for 20-25 minutes or until the edges are golden brown.
Let the treats cool completely on a wire rack before serving.