Combine the mashed potatoes, egg, Monterey Jack cheese, chives, and 2 tablespoons of the flour in a large bowl. If your mashed potatoes are loose, stir in additional flour for a stiffer consistency. Season the mixture with salt and freshly ground black pepper and stir in any add-ins you might be including.

Using a ⅓-cup dry ingredient measure, divide the potato mixture into 10 even portions and shape them into rough balls.

Combine the breadcrumbs and Parmesan cheese in a shallow dish. Place each potato ball into the breadcrumbs and flatten it to form the mixture into a 3-inch patty. Carefully flip the cake over and coat the other side with crumbs as well. Flatten the edges of the cakes with your hands or a spatula so that each one is a straight-sided disk. This will help to prevent the potato pancakes from spreading out too much while cooking.

Heat an electric griddle to 350˚F or pre-heat a large skillet over medium-high heat. Add a glug of vegetable oil and a tablespoon of butter to the griddle or skillet. Add the potato pancakes, cooking in batches if necessary and cook for 6 to 8 minutes on each side until lightly browned. Flip the cakes over carefully - they will be soft and delicate until both sides are browned. When browned on both sides and heated through in the center, transfer the potato cakes to a plate lined with parchment paper or paper towels. Repeat with the second batch of potato pancakes, adding additional oil and butter as needed.

Garnish with fresh chopped chives and serve warm with sour cream if desired.