In large bowl, stir together mashed potatoes,parsley,season with salt and pepper. Pur flour in a shallow bowl;season with salt and pepper. Whisk egg and water. In third shallow bowl,place fresh breadcrumbs.
Form potato mixture into 3/4 by 2 logs. Roll in flour,shaking off excess,dip in egg wash,then roll in breadcrumbs to coat.
In heavy medium saucepan,heat vegetable oil over med-high unti hot. In batches,fry croquettes until golden brown on all sides,about 2 mins. per batch,turning as needed. Drain on paper towels.