Place dried mushrooms in a bowl, and pour 4 cups boiling water over them. Let sit 30 minutes to allow flavors to infuse. Make a bouquet garni: Wrap rosemary and thyme sprigs in cheesecloth, and tie with kitchen twine; set aside. Lift out mushrooms with a slotted spoon, and place in another bowl. Press mushrooms to release any retained stock, and pour liquid back into bowl; set mushrooms aside. Strain mushroom liquid through a fine-mesh sieve lined with a paper towel. You should have about 4 cups of mushroom stock; set aside.
Melt 5 tablespoons butter in a large saucepan over medium heat. When bubbling, add flour. Cook, stirring until mixture begins to brown, about 3 minutes. While whisking, slowly pour in mushroom stock. Continue cooking, whisking constantly, until the mixture bubbles and becomes thick. Stir in cream and reserved bouquet garni. Reduce to a gentle simmer, and cook 30 minutes, stirring occasionally.
Meanwhile, in a large ovenproof skillet, heat remaining 2 tablespoons butter over medium heat. Add onion, and cook until it begins to soften, about 3 minutes. Add button mushrooms, and cook until they release their juices. Add shiitakes, reserved mushrooms, and 2 teaspoons chopped thyme, and cook until all are tender, about 5 minutes. Add cream sauce to skillet, and stir to combine. Season with salt and pepper, and set aside.
Preheat oven to 375 degrees. Bring a large pot of water to a boil. Add pasta; cook until very al dente, 2 to 3 minutes less than manufacturer's instructions. Transfer noodles to a colander, and rinse with cold water to stop the cooking. Stir noodles into mushroom mixture. Sprinkle with grated cheese, and bake in skillet until browned on top and mixture is bubbling, about 30 minutes. Transfer dish to a wire rack to cool 5 minutes before serving.
If you don't have a large ovenproof skillet, you can prepare the mushroom sauce in any large skillet. Cook the pasta and add it to the mushroom sauce, then transfer noodles and sauce to a buttered 9-by-13-inch baking pan, and bake.