In a large bowl, combine the potatoes, salmon, 1 egg, zest, and parsley.

Put the flour in a shallow bowl and season with salt and pepper. In another shallow bowl, whisk the remaining egg with 1 tablespoon water. Place the bread crumbs in a third shallow bowl.

Using wet hands, form the potato mixture into 3-inch patties or sticks. Dip the patties in the flour, shaking off any excess, dip them in the egg wash, and then roll them in the bread crumbs, pressing the crumbs on to form a crust.

Coat the bottom of a large skillet with oil; working in batches, fry the croquettes until golden brown on both sides, about 4 to 6 minutes total. Drain on paper towels and serve immediately.