Combine the mashed potatoes, egg, cheddar cheese, chives, flour, sea salt, and freshly cracked pepper in a bowl; mix until well combined.
Roll the potato mixture into like-sized round balls.
Roll the potato balls in the panko crumbs until evenly coated.
Place in the refrigerator for 30 minutes. Side Note: Don't skip this step; it helps the panko adhere to the potato balls.
Heat the oil in a large skillet. Fry each croquette in shallow oil (enough to fill the skillet ½-inch), until browned on all sides. Make sure to cook in small batches, giving each croquette at least 2 inches of space around to avoid overcrowding the skillet. This prevents the croquettes from falling apart while frying.
Remove from the oil and place on a wire cooling rack.
Serve immediately with sour cream and chives on the side, if desired. Enjoy.