Preheat oven to 350º F and line baking sheet with parchment paper.
In a large bowl or mixer, beat together peanut butter and pumpkin puree until smooth and creamy. Beat in the egg until it is fully incorporated.
Alternately add flour and water to peanut butter mixture, beginning and ending with the flour. Beat until dough begins to come together and is no longer too sticky.
Turn dough out on a lightly floured surface and knead for 2 minutes, or until fully formed into a ball.
Roll dough out to 1/4-1/2-inch thickness and use your cookie cutter(s) to cut out desired shapes and amounts of treats. Transfer to baking dish and place in oven.
Bake for 20-25 minutes (baking time depends on size), or until cookies are golden brown.