Combine the leftover colcannon, shredded extra sharp white cheddar, sea salt, freshly cracked pepper, to taste, and the egg in a bowl. Mix until well combined.
Pour the panko crumbs on a plate. Shape the potato mixture into golf ball-sized balls. Coat each side of the potato pancake in the panko crumbs evenly, while gently flattening, then place them on a large plate.
Place in the refrigerator for 20-30 minutes. Side Note: This helps the panko stay adhered to the potato.
Heat half of the olive oil and half of the butter in a large skillet over medium heat. Carefully place each potato croquette into the hot skillet and cook, without disturbing, for 4-5 minutes or until golden brown.
Carefully flip the croquette over and add the remaining butter and oil to the skillet. Continue cooking for another 3-4 minutes or until golden brown.
Remove from the skillet and serve immediately. Enjoy.