Melt three tablespoons of butter in a large, thick-bottomed skillet.
Slice two large onions into thin (⅛-inch) rounds and add them to the skillet along with ½ tablespoon of sugar. Sauté the onions, covered, over medium to medium-low heat for 45 minutes, stirring occasionally.
Next, add 12 ounces of sliced mushrooms to the pan, along with dill, nutmeg, salt and black pepper.
Sauté the mushrooms, onions and spices for 10 minutes. Last, squeeze the juice from half a lemon into the skillet, stir and remove the pan from the heat.
Lightly dust a hard surface and gently roll out one sheet of thawed puff pastry into a 10" x 13" rectangle. Place the puff pastry onto a baking sheet that has been lined with parchment paper.
Spoon the mushroom and onion mixture over top of the puff pastry leaving a ½- inch edge. Grate one cup of Parmesan cheese over top of the puff pastry and bake for 20 minutes at 400° or until golden brown and bubbly.
Garnish the Caramelized Onion and Mushroom Puff Pastry with fresh dill if desired.
Slice and serve warm.