Preheat the oven to 400 degrees. In a large saucepan, combine the water, milk, butter, salt, cumin, and onion powder. As soon as the mixture comes to a boil, remove the saucepan from the heat and add the potato flakes; mix until smooth. Add the parsley and egg and mix again until smooth.
Form the mixture into 8 equal-sized patties. Brush both sides with the oil and place on a large nonstick cookie sheet that has been sprayed with nonstick cooking spray. Bake for 25 minutes, turning once halfway through the cooking.