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 evenly with the panko crumbs, gently flatten them, then place them onto a large plate.
Place the plate into the refrigerator for 20-30 minutes.
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 3-4 minutes or until golden brown.
Remove from the skillet and serve immediately. Enjoy.