Combine the mashed potatoes, egg, cheddar cheese, chives, flour, sea salt, and freshly cracked pepper together 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 into 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 pan 1/2-inch) until brown on all sides. Make sure to cook in small batches, giving each croquette at least 2 inches of space around it to not overcrowd the pan. This prevents the croquettes from falling apart while frying.
Remove from oil and place on a paper towel lined plate to remove excess grease. Sprinkle with freshly cracked sea salt and black pepper, to taste.
Serve immediately with sour cream and chives on the side, if desired. Enjoy.