When my mom would have leftover mashed potatoes, she would often make what she called potato pancakes: not a sweet pancake but a savory one.
She mixed a few chopped onions into the mashed potatoes, formed them into pancakes, and then heated them in a skillet.
I did something similar after Xmas except I used the leftover aromatics I stuffed into my turkey.
Roughly equal parts diced carrot, bell pepper, and red onion with chopped parsley
Leftover mashed potatoes
Salt and pepper to taste
Place mashed potatoes in a mixing bowl and fold in the aromatics. Mix it all together and form into a thick pancake. Lightly oil a skillet on medium-high heat, slap the pancake down till you get a good crust on the bottom, and then flip it to get a tasty crust on the other side.
Here's what the pancake looks like when it's in a small cast iron skillet.