In a large bowl, combine the mashed potatoes, eggs, and flour. Season to taste with salt. (If your mashed potatoes weren’t seasoned, make sure to go generous on the salt.) Stir to combine.
Place the panko bread crumbs in a bowl. Drop about a tablespoon of the mixture into the crumbs, then roll to coat. Use your hands to shape into a tater tot shape. Place on a plate or baking sheet. Continue with the rest of the potatoes.
Heat about an inch of oil in a heavy duty skillet over medium heat. (I like to use my cast iron skillet.) Heat the oil to 350ºF.**
Place the tots in the hot oil in batches, cooking until they are golden brown, flipping often. Remove to a paper towel lined plate and immediately sprinkle with coarse salt.
Continue until all of the tater tots have been cooked.
