On a lightly floured surface, roll each puff pastry sheet into a 12-in. square. Place one square in a 10-in. quiche dish; set dish and remaining pastry aside.
In a large skillet, melt butter. Add potatoes, onion, salt and pepper; cover and cook for 10-12 minutes or until potatoes are tender and golden brown, stirring occasionally. Set aside.
In a large bowl, beat the eggs, parsley, water, salt and pepper. In a 10-in. skillet, melt 1 tablespoon butter; add half of the egg mixture. Cook over medium heat. As eggs set, lift edges, letting uncooked portion flow underneath. Continue cooking until set. Slide omelet onto a baking sheet. Repeat with remaining butter and egg mixture to make a second omelet.
Sprinkle 1 cup cheese over prepared pastry. Top with one omelet and half of the potato mixture. Layer with ham and the remaining potato mixture, cheese, omelet and puff pastry. Trim pastry to fit dish; seal and flute edges.
In a small bowl, combine egg and water; brush over pastry. Bake at 375° for 30-35 minutes or until golden brown. Let stand for 10 minutes before serving. Yield: 8 servings.