In a large bowl, whisk together the eggs, 1 tablespoon water and 1/2 teaspoon each salt and pepper. Heat 2 tablespoons olive oil in a 10-inch non-stick skillet over medium heat. Add the potatoes and cook, covered, stirring occasionally, for 8 minutes. Add the onion and cook, covered, until the potatoes are golden brown and tender, 4 to 5 minutes more. Add the kielbasa and cook, uncovered, tossing occasionally, until golden brown, about 5 minutes; transfer the potato mixture to a plate. Add the egg mixture to the skillet and cook, stirring every few seconds with a rubber spatula, to desired doneness, 2 to 3 minutes for medium-soft eggs. Fold in the potato mixture, cheese and parsley.