To prepare the dough, combine the flours and salt in a large bowl.

Add the butter and, using a pastry blender (or two forks), blend together until the butter becomes the size of small pebbles.

Pour the water over the mixture and knead until a dough forms, adding another teaspoon of water if needed.

Cover with plastic wrap and refrigerate for one hour, or up to two days.

To prepare the filling, heat the olive oil in a large sauté pan over medium heat. Add the onions, tossing them to coat with oil. Reduce the heat to medium-low and cook until nicely caramelized, about 25 minutes. 

Meanwhile, rinse the mushrooms in a colander and let the water drain out.

Once the onions have cooked, mix in the mushrooms, season with salt and pepper, and cook for another two to three minutes. Remove from heat.

In a bowl, combine the mushroom mixture with the herbs, mozzarella, and feta cheese.

Preheat oven to 400°F. Line a baking tray with Gefen Parchment Paper and set aside.

Cut the chilled dough in half, and roll each piece into a 10-inch round.

Place onto the prepared baking tray and spoon half of the filling in the middle.

Fold the edges over in uneven pleats and brush the sides with egg wash.

Bake at 400° F for 45 minutes, until nicely browned.

Cut into wedges, sprinkle with a generous amount of grated Parmesan cheese, and serve with a side of salad.