This dish was a hit in our home and though it looks time consuming, it really wasn't. You can even make it the night before, refrigerate and bake as normal the next day. We had this for dinner and we ALL loved it. Lots of flavor and a perfect comfort food.
Preheat oven to 375 degrees F (190 degrees C). On lightly floured surface, roll each sheet of puff pastry into a 12 inch square. Lay 1 sheet puff pastry into a 10 inch pie plate; set aside.
In a 10 inch skillet, melt 1/4 cup butter until sizzling. Add potatoes, onion, 1/4 teaspoon salt and 1/4 teaspoon pepper. Cover and cook over medium-high heat, turning occasionally, until potatoes are lightly browned and crisply tender, about 12 to 15 minutes. Set aside.
In a new skillet, melt 1 tablespoon butter until sizzling. Meanwhile, in a small bowl, stir together all omelet ingredients except remaining 1 tablespoon butter. Pour half of omelet mixture (3/4 cup) into heated skillet. Cook over medium heat. As omelet mixture sets, lift slightly with spatula to allow uncooked portion to flow underneath. Continue cooking until set, about 2 to 3 minutes. Slide omelet onto cookie sheet. Repeat with remaining butter and omelet mixture.
Layer ingredients into pie plate on top of puff pastry in the following order: one of the omelets, 4 ounces ham, half of fried the potatoes, 1 cup shredded cheese, remaining potatoes, ham, cheese and 2nd omelet. Top with remaining sheet of puff pastry. Press together edges of both sheets of puff pastry to form a rim; trim off excess. Crimp or flute edges. In small bowl, stir together 1 egg and 1 tablespoon water; brush over puff pastry.
Bake 30 to 35 minutes or until golden brown. Let stand 5 minutes; cut into wedges.
To keep them from budding, place an apple in the bag with potatoes.
Wrap celery in aluminum foil when putting in the refrigerator, and it will keep for weeks.
Refrigerated apples last up to 10 times longer than those left at room temperature. To prevent apples from speeding up the ripening process of other items in your produce drawer, store them in a plastic or brown paper bag.