Preheat oven to 350°F.
Place 4 cups of old fashioned rolled oats into the food processor fitted with the metal blade. Grind oats until flour forms. Transfer oat flour into a large bowl.
Drain the sardines and add them to the empty food processor, add pumpkin, peanut butter, and egg, process until well-mixed.
Add 3 cups of oat flour to the liquid mixture, one cup at a time and process each time until the flour is incorporated.
If the dough is still wet, sprinkle a little bit more flour (up to ¼ cup more) and process until the dough resembles pie dough.
Sprinkle some oat flour on a cutting board and turn the dough out, knead or shape into a disk and roll out to about ¼" thick. Use the rest of the oat flour for kneading and rolling as needed to keep the dough from sticking to the board.
Cut with a 2” bone shape cookie cutter, place on a baking sheet about ½” apart, and bake for 40 minutes.
Turn off the oven when done and leave them in the oven to dry overnight.
Store in an airtight container or Ziploc bag.