First make the filling: Drain the dried mushrooms, reserving the soaking liquid, and mince. In a skillet cook the shallots in the oil over moderate heat, stirring until they are softened. Add the fresh mushrooms and salt and pepper to taste and cook the mixture, stirring, until it is dry. Add the dried mushrooms and the garlic, cook the mixture, stirring, until it is dry, and transfer it to a bowl. Add the mozzarella, the Parmesan, and salt and pepper to taste to the mushroom mixture and stir the filling until it is well combined. Make the ravioli: Trim the ends of the dough and cut the dough crosswise into 2 pieces, 1 piece 1 1/2 inches longer than the other. Put a rounded teaspoon of the mushroom mixture in 2 rows on the shorter piece, spacing them about 1 inch from the edges and with their centers about 1 1/2 inches apart. Brush the dough around the filling with water, put the longer piece of dough on top, and press it gently around the mounds of filling. With a fluted pastry wheel or knife cut the dough between the mounds. Arrange the ravioli in one layer on a baking sheet sprinkled with flour and let dry one hour.
When ready to cook the ravioli, bring a large pot of salted water to a boil. Add ravioli and cook, stirring, for 5 minutes, or until it is just tender, drain it in a colander and transfer it to a large bowl. Then in a small saucepan melt the butter and add the butter to the ravioli, tossing to coat it well. Transfer to serving dish. In another saucepan combine the heavy cream, 1/2 cup of the reserved mushroom soaking liquid, strained through a double thickness of rinsed and squeezed cheesecloth, and simmer the mixture, stirring occasionally, until it is slightly thickened. Season the sauce with salt and pepper to taste. Top the ravioli evenly with the sauce and sprinkle with the parsley and the Parmesan before serving.