In a large mixing bowl, combine the cold mashed potatoes, shredded chicken, flour, eggs, Parmesan cheese, minced garlic, fresh herbs, paprika, oregano, salt, and pepper. Mix thoroughly until well combined.
Cover the mixture and refrigerate for at least 30 minutes to firm up, making it easier to handle.
In a separate bowl, mix together the panko breadcrumbs, regular breadcrumbs, garlic powder, and onion powder for the coating.
Heat vegetable oil in a deep fryer or large pot to 350°F (175°C).
Remove the potato-chicken mixture from the refrigerator. With lightly floured hands, take about 1/4 cup of the mixture and form it into a ball, then flatten slightly and use your thumb to create a hole in the center to form a doughnut shape.
Carefully coat each doughnut in the breadcrumb mixture, pressing gently to ensure the coating adheres well.
Working in batches of 3-4 doughnuts at a time, carefully lower them into the hot oil using a slotted spoon.
Fry for 3-4 minutes until golden brown and crispy, turning occasionally for even cooking.
Remove with a slotted spoon and place on paper towels to drain excess oil.
For the optional dipping sauce, mix all sauce ingredients in a small bowl until well combined.
Serve the doughnuts warm with the dipping sauce on the side.