1-2 pounds assorted fresh mushrooms, such as button, cremini, and shiitake, brushed clean, trimmed, and coarsely chopped
1/2 cup freshly grated Pecorino Romano cheese, plus more for serving
1/2 cup ricotta cheese
1/2 teaspoon coarse salt
1/4 teaspoon freshly ground pepper, plus more for serving
pinch of fresh thyme
pinch of fresh thyme, for serving
In a small bowl, combine porcinis and water. Let stand until soft, about 30 minutes. Strain, reserving 1/4 cup of the soaking liquid. Coarsely chop mushrooms; set aside.
In a large skillet, heat oil over medium-high heat. Add shallots, and cook until translucent, about 2 minutes. Stir in parsley, and cook 1 minute more. Add fresh and dried mushrooms and cook, stirring frequently, until mushrooms first release their liquid and then liquid evaporates, about 10 minutes. Add the 1/4 cup reserved soaking liquid. Cook, stirring, until liquid evaporates, about 5 minutes more. Transfer to a bowl, and cool briefly before stirring in Parmesan and ricotta. Season with salt and pepper.
Bring a large pot of salted water to a boil. Add about 6 ravioli per serving, and cook until tender but al dente, about 2 minutes (slightly longer if frozen). In a skillet, melt 1 tablespoon of butter and 1 teaspoon of oil with 1 sprig of thyme for each serving. When ravioli are done, use a slotted spoon to remove from boiling water. Drain well, and transfer to skillet. Toss in butter, and divide among warm bowls. Top with shaved Parmesan and freshly ground pepper.