In a pan, heat 2 tablespoons of olive oil over medium heat. Add the minced garlic and sauté until fragrant.
Add the rehydrated porcini mushrooms to the pan, cooking them until they’re tender and any liquid has evaporated. Once cooled, chop them finely.
Combine the minced woodcock meat, finely chopped mushrooms, and grated Parmigiano-Reggiano in a bowl. Mix well, then set the bowl in the fridge.
On a clean work surface, mound the flour and create a well in the center. Crack the eggs into the well. Add a pinch of salt and olive oil to the eggs. Using a fork, gently beat the eggs, gradually incorporating the surrounding flour. Continue mixing until a sticky dough begins to form.
Once the dough starts coming together, use your hands to knead it. Knead for about 8–10 minutes, or until the dough is smooth and elastic. If the dough is too sticky, sprinkle it with a bit more flour as you knead. If it’s a little dry, wet your hands with some water and continue kneading until smooth.
Shape the dough into a ball and wrap it tightly in plastic wrap. Let it rest at room temperature for at least 30 minutes; this allows the gluten to relax, making the dough easier to roll out.
After resting, divide the dough into four even portions. Using a KitchenAid pasta attachment, pass each portion through the machine, starting on setting 1 and gradually working up to setting 5. Each portion should roll out into sheets approximately 2 feet long and 10 inches wide.
Lay the sheets onto a lightly floured tablecloth to prevent sticking. Lightly flour the sheets of pasta dough as well.
Lay out a sheet of pasta and place small mounds of filling (about 1 teaspoon each) evenly spaced along the sheet.
Lightly brush around the filling with water or egg wash to help seal the ravioli.
Carefully place another sheet of pasta over the filling, pressing around each mound to seal and remove any air pockets.
Cut the ravioli using a pasta cutter or knife, ensuring each piece is well sealed.
Repeat with the remaining dough and filling.
Bring a large pot of salted water to a boil. Add the ravioli and cook for 2–3 minutes, or until they float to the surface.
Meanwhile, in a large skillet, melt the butter over medium heat. Add the sage leaves and cook until the butter is golden brown and the sage is crispy.
Drain the cooked ravioli and add them to the skillet with the sage butter. Toss gently to coat.
Serve the ravioli hot, garnished with additional grated Parmigiano-Reggiano and a sprinkle of black pepper. Enjoy!