Direction

1. Pulse flour and salt in a food processor until combined, about 2 pulses. Add eggs; pulse until small dough crumbs form and mixture comes together easily when squeezed, about 8 pulses. Transfer crumbs to a clean work surface. Press into a mass, and knead until dough is smooth and elastic, about 10 minutes. (If dough is too sticky, sprinkle with additional flour, 1 teaspoon at a time; if dough is dry, too tight to knead, or cracking, lightly wet hand with water, and knead into dough.)
2. Wrap dough tightly in plastic wrap; let rest at room temperature at least 1 hour or up to 2 hours, or let rest in refrigerator up to 12 hours. (If refrigerating, let come to room temperature before rolling.)
3. Remove soaked porcini mushrooms from water, reserving soaking liquid for another use. Finely chop porcini mushrooms; set aside.
4. Heat oil in a medium skillet over medium-high until shimmering. Add 2 cups fresh mushrooms, and stir to coat in oil; spread in an even layer. Cook, undisturbed, until bottom sides are browned, about 4 minutes. Stir and sprinkle with 1/4 teaspoon salt and pepper; cook, stirring occasionally, until lightly browned all over, about 4 minutes. Reduce heat to medium. Add garlic, thyme, and chopped porcini mushrooms; cook, stirring often, until mixture is fragrant and dry, 1 to 2 minutes. Add sherry; cook, stirring constantly and scraping bottom of skillet using a wooden spoon to release browned bits, until mostly evaporated, about 30 seconds. Add butter and lemon zest; cook, stirring constantly, until butter is melted, about 1 minute. Remove from heat, and transfer mixture to a small bowl. Refrigerate, uncovered, until cooled, about 20 minutes.
5. Transfer cooled mushroom mixture to a food processor, and add ricotta, mascarpone, Parmesan, and remaining 1/4 teaspoon salt; pulse until mushrooms are finely chopped and mixture is creamy, about 5 pulses, stopping to scrape down sides of processor as needed. Cover Mushroom Filling, and refrigerate until ready to use.
6. Unwrap dough, and divide evenly into 4 portions. Place 1 dough portion on a clean work surface; cover remaining dough portions using a clean kitchen towel. Shape dough into a rectangle; press dough to flatten using heel of hand. Starting with widest setting of a pasta machine, pass dough through pasta machine 3 times. Fold outer tapered ends of pasta sheet in toward center, and press dough so that the width of the pasta sheet is similar to the width of the pasta roller. Pass pasta sheet through widest setting 3 more times, folded edge first. Continue rolling pasta through machine, reducing roller width 1 notch at a time, until sheet is about 1/16-inch thick and you can see the outline of your hand through the sheet (18- x 5-inch rectangle). Lay sheet on a work surface lightly dusted with flour; trim uneven edges. Repeat process with remaining 3 dough portions.
7. Bring a large pot of salted water to a boil over high. Meanwhile, spoon or pipe 2 teaspoons Mushroom Filling on 2 of the pasta sheets, forming 2 rows of 6 on each sheet, about 1 inch apart. Drape 2 remaining pasta sheets over filling, lining up sheets. Press dough around each mound to seal and press out air pockets. Using a fluted pastry cutter or a sharp knife, cut between mounds to form squares. Place ravioli on a baking sheet lined using a clean kitchen towel.
8. Melt butter in a large, deep skillet over medium, stirring often, until melted, about 2 minutes. Cook over medium, stirring constantly, just until milk solids sink to bottom of skillet and begin to darken but are not browned, 3 to 4 minutes. Add sage leaves; cook, stirring constantly, until sage leaves darken and crisp and butter browns, 1 to 2 minutes. Using a slotted spoon, transfer sage to a small plate lined using paper towels. Add 1 cup fresh mushrooms to browned butter; cook, stirring often, until tender, 3 to 4 minutes. Season with additional salt to taste.
9. While Sauce is cooking, add ravioli to boiling water in pot. Cook, stirring occasionally, until tender, about 5 minutes. Ladle about 1/2 cup cooking water into Sauce in skillet; transfer cooked ravioli to skillet using a slotted spoon or a spider. Increase heat to medium-high; cook, gently swirling and shaking skillet, until butter is creamy-looking, adding additional cooking water, about 1/4 cup at a time, as needed. Remove from heat, and season with additional salt, if needed. Serve immediately.