In a large bowl, whisk together the eggs, water, salt and pepper.

Heat 2 tablespoons olive oil in a 10-inch non-stick skillet over medium-high heat. Add the potatoes and cook, covered, stirring occasionally, for 10 to 15 minutes. Add the onion and cook, covered, until the potatoes are golden brown and tender, 10 minutes more. Add the kielbasa and cook, uncovered, tossing occasionally until golden brown, about 15 to 20 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, (6 to 8 minutes for medium-soft eggs.) Fold in the potato mixture and cheese. Cook for a few minutes more or until cheese is melted, 5 minutes.

Garnish with chopped fresh parsley if desired.