Step 1

In a large bowl, stir together mashed potatoes and parsley; season with salt and pepper. In a shallow bowl, place flour; season with salt and pepper. In another shallow bowl, whisk egg with 1 tablespoon water. In a third shallow bowl, place 1 1/2 cups breadcrumbs.

Step 2

Form potato mixture into 3/4-by-2-inch logs. Roll in flour, shaking off excess, dip in egg wash, then roll in breadcrumbs to coat. In a heavy medium saucepan, heat 1 1/2 inches vegetable oil over medium-high until hot. In batches, fry croquettes until golden brown on all sides, about 2 minutes per batch, turing as needed. Drain on paper towels.