Preheat your oven to 400 F (200 C). Line a baking sheet with parchment paper or lightly grease it.
If your mashed potatoes are freshly made and warm, let them cool until they are room temperature. Warm potatoes are too loose.
In a large bowl combine the cooled mashed potatoes, shredded cheddar, eggs, flour, Parmesan, garlic powder, salt, pepper, and chives if using. Mix until everything is evenly distributed. The mixture should hold together when pinched.
Place the panko breadcrumbs in a shallow bowl. Using a tablespoon or small cookie scoop, portion the potato mixture into rounded mounds. Gently shape each mound into a ball or slightly flattened puff.
Roll each puff lightly in the panko breadcrumbs to coat. For extra crispiness, press the panko on so it adheres well.
Arrange the puffs on the prepared baking sheet, leaving a little space between them. Brush the tops lightly with melted butter to help with browning.
Bake for 18 to 22 minutes, or until the outsides are golden brown and firm. If you want them extra crisp, broil on high for 1 to 2 minutes while watching closely.
Remove from the oven and let cool for a few minutes before serving. These are lovely warm, with a little sour cream, ketchup, or your favorite dipping sauce.
Leftovers can be stored in an airtight container in the refrigerator for up to 3 days. Reheat in a 375 F oven for about 8 to 10 minutes to restore crispness.