In a large bowl, combine the chickpea flour, puree pumpkin, and peanut butter with your hand and knead it until it forms a dough ball. If the dough feels very sticky, keep adding chickpea flour 1 tablespoon at a time until the dough is smooth and not sticky. It should be the consistency of play-doh.
Once the dough has come together, cover it in plastic wrap and keep it in the fridge for 1 hour. This will make the dough stiffer and easier to cut shapes out of.
Once the dough has been chilled in the fridge for an hour, take it out of the fridge and plastic wrap.
Line a cookie sheet or baking pan with parchment paper and set it close by.
Sprinkle chickpea flour liberally on the counter you are rolling out the dough on. Dust the rolling pin as well.
Sprinkle a bit of chickpea flour on the dough and rub it gently on until there is a light coating on it, then roll out the dough to about ¼ inch to ½ inch thickness.
(Note: If the dough is still sticky, it might stick to the counter - to address that, dust the dough frequently on both sides and flip it often while you are rolling it out)
Use a cookie cutter and cut out shapes in the dough. It is crucial to dip the cookie cutter in the chickpea flour in between each cooking cutting to prevent the dough from sticking to it. If you don't have a cookie cutter, you can cut them into squares or rectangles with a knife.
Place the cut out shapes on the parchment paper with about ½ inch between each dog treat.