Preheat the dog bone waffle iron. Alternatively, you may cook the treats as small pancakes in a skillet on the stovetop.
In a mini food processor, combine the chicken and rice. Process until the pieces are uniformly very small. Add the parsley, and pulse until the mixture is like a course sand. Add the egg, and process to form a wet purée. Add the rice flour and pulse to combine. At this point, if needed, you can add a touch more rice flour or a trickle of water until the mixture is a soft, slightly sticky dough. (I typically need to add 2-3 teaspoons of water. If you have leftover chicken broth on hand, feel free to use that.)
Lightly spray the cooking surface of the dog treat maker or skillet with non-aerosol cooking oil. Heat the skillet, if using, over medium heat. Add a tablespoon of dough to the preheated treat maker and close the lid; or add the dough to the skillet, spreading into an even layer.
Cook the treats for about 7 minutes total, using tongs or a fork to gently pry from the mold, or a spatula when cooking on the stovetop, to flip once the bottoms are lightly golden. When cooked through and golden on both sides, remove to a plate to cool. Repeat with the remaining dough.
Storage: Once cooled, store in an airtight container or zip-top bag in the refrigerator for up to a week. The bones freeze well too and can be given to your dog straight from the freezer.
Notes
Helpful tips when using dog bone waffle iron: I use a dinner knife to spread the dough into the mold, leveling it at the top. This ensures the mold is evenly and fully filled, making for the best shaped bones. Once I have all the molds filled, I close the lid. Don't worry too much about having the lid open while you fill all the molds, as it does take a few minutes. Start checking the bottoms of the molds you filled first, flipping when golden and gently pressing back into the mold. The treats are hard to overcook; you simply don't want to burn them.