Prepare the pastry according to the recipe, and roll out to even thickness. With a water glass or cookie cutter, cut into 2 1/2-inch diameter circles.
In a 12 to 14-inch saute pan, heat the oil over high heat until smoking. Add the mushrooms and saute over high heat until browned. Add the garlic, parsley, mascarpone and salt and pepper to taste, stir in, and remove from heat.
Spoon some of the filling onto one half of each of the pastry circles. Fold each circle over on itself and press the edges to make a seal.
In a large, heavy-bottomed skillet, heat about 1/2 cup olive oil over high heat until almost smoking. Fry the pastries in the oil until golden-browned on both sides. Remove with a slotted spoon to a plate lined with paper towels, then serve.
In a large bowl, combine wine, water and yeast and stir until dissolved. Add the honey, salt and olive oil and mix thoroughly. Add 1 cup of flour and mix with a wooden spoon until it becomes a loose batter. Add 2 more cups of flour and stir with the spoon for another 2 to 3 minutes, to incorporate as much of the flour as possible.
Bring the dough together with your hands and turn it out onto a floured board or marble surface. Knead for about 6 to 8 minutes, until you have made a firm, smooth dough. Place it in a clean, lightly-oiled bowl and cover it with a towel. Let it rise in the warmest part of the kitchen for 45 minutes.
Recipe copyright 2000, Mario Batali. All Rights Reserved.