In a large bowl, stir together the mashed potatoes, scallions, cheese, eggs, and a pinch of salt and pepper until well combined.
Place the breadcrumbs in a separate large bowl.
Scoop out about 3 tablespoons of the mashed potato mixture and roll it into a ball then roll the ball in the breadcrumbs. Repeat the rolling and breading process with the remaining mashed potato mixture.
Line a baking sheet with paper towels. Add the vegetable oil to a large heavy-bottomed stockpot set over medium heat and attach the deep-fry thermometer.
Once the oil reached 360°F, add a few of the mashed potato balls and cook them, turning occasionally, until they’re golden brown.
Using a slotted spoon or colander, transfer the mashed potato balls to the paper towel-lined plate and immediately season them with salt.
Add the remaining mashed potato balls to the oil, returning the oil to 360°F between each batch.
Serve the mashed potato balls with leftover cranberry sauce or gravy for dipping.