In a large bowl, mix the mashed potatoes with the grated Parmigiano Reggiano, lemon zest, and lemon juice; season with salt and pepper. In a shallow bowl, stir together the flour, a pinch of salt, and a couple grindings of pepper; in a second shallow bowl, whisk together the eggs with a tablespoon of water; place the breadcrumbs in a third shallow bowl.

Form the potato mixture into 2 by 3/4-inch logs. Roll the logs in the flour, shaking off the excess, dip in the egg wash, then roll in the breadcrumbs to coat.

Heat 1-1/2 inches of oil in a shallow heavy-bottomed pan over medium-high heat. You can test if the oil is hot enough for frying by dropping a cube of bread in the oil. It should sizzle and float to the top immediately. Fry the croquettes in batches until golden brown on all sides, about 1 minute per batch, turning halfway through cooking time. Drain on paper