a large pastry bag, pasta machine and a 2-to-3-inch round fluted cutter
For the dough: Mound the flour on a large cutting board and make a wide well in the middle. Add the eggs and olive oil and season with 1/2 teaspoon salt. Beat the eggs with a fork, then use the fork to break the wall of the well and incorporate the flour into the eggs. Gather the dough into a ball; don't worry if there are lumps.
Using the heels of your hands, push the dough away from you, then fold it back over itself and push again (put your whole body into it!). Continue kneading until the dough is smooth and supple, 10 to 15 minutes. Wrap the dough in plastic wrap and let rest at least 1 hour at room temperature.
For the filling: Drizzle olive oil into a large deep pan. Add the pancetta, place over medium-low heat and cook until crisp. Add the garlic and cremini, oyster and shiitake mushrooms, season with salt and saute until the mushrooms are soft and golden, about 5 minutes. Add the white wine and let cook until completely reduced. Remove from heat and let cool slightly.
Mix the ricotta Parmigiano-Reggiano and , taleggio in a large bowl. Stir in the mushroom mixture, eggs and parsley and season with salt. Transfer the filling to a large pastry bag and refrigerate if not using immediately.
Cut the dough into four pieces. Flatten one piece slightly, then run it through the widest setting on a pasta roller twice, dusting with flour in between if it feels sticky. Fold the length of dough into thirds and run it through the roller two to three more times. Continue running the dough through the roller, reducing the width setting between each run, until you reach the second-to-last setting and the dough is about 1/16 inch thick. Repeat with the remaining pieces of dough. Layer half of the dough sheets between parchment paper, wrap in plastic wrap and freeze for up to 1 month (you'll only need half of the dough for the ravioli recipe).
For the ravioli: Place the lengths of dough on a floured surface. Lightly brush the lower half of each strip (the part closest to you) with water. Snip the corner off the pastry bag; pipe 1-inch balls of filling, 2 inches apart, onto the lower half of each strip. Fold the dough over the filling to meet the bottom edge. Press around each ball of filling with your index fingers, making sure there are no air bubbles. Cut out the ravioli using a 2-to-3-inch round fluted cutter. Pinch around the cut edges of the raviolis and transfer to a baking sheet dusted with semolina.
For the sauce: Add chicken stock and butter to a large deep pan, season with salt and cook until the sauce is thickened, reduced by half and looks velvety. Season with more salt, if necessary.
Bring a large pot of well-salted water to a boil; add the ravioli and cook 3 to 4 minutes. Transfer with a skimmer or slotted spoon to the pan with the sauce. Bring the sauce to a boil, shaking the pan. Sprinkle in the sage and remove from the heat. Add the Parmigiano-Reggiano and swirl to combine. Serve garnished with more Parmigiano-Reggiano.