For the filling, heat tablespoons of the butter over medium heat in a 10 to 12-inch sauté pan until it foams then subsides. Add the onions and cook for about 7 minutes or until soft and golden. Add the sausage and let cook until they are cooked through. This should take about 10 to 12 minutes.
Transfer mixture to a food processor and pulse until finely chopped. Transfer mixture again to a medium-sized bowl and add ricotta, goat cheese, oregano, nutmeg, and 1/4 cup parsley, then mix well.
To make the pasta, mix the flour and salt. Form a mound with the flour mixture and make a well in the center. Place the egg yolks in the well and, using a fork, mix the flour and eggs together. Gradually bring the flour from the sides, and continue adding the flour until the dough comes together and all the flour is incorporated. Knead the dough until smooth and elastic. You should knead no shorter than 10 minutes. If the dough is sticking, add a little flour to the work surface. It should be a bit sticky. Shape the dough into a disc, wrap in plastic wrap, and place in the refrigerator to rest for at least 30 minutes. You can do this a few days in advance.
Divide the dough into four equal portions. Cover the remaining three portions with a clean damp towel to keep it from drying out. Lightly dust the dough with flour and pass it through a pasta machine at its widest setting. Lay the dough on a lightly floured surface and fold on top of itself to make the ends meet. Pass it a second time through the pasta machine set on the same setting. Adjust your pasta machine down a setting and pass the sheet through the pasta machine. Fold it in half again and continue passing it through, reducing the setting each time until you reach the lowest setting. Keep pasta covered until ready to use.
Lay two of the pasta sheets side by side and spoon rounded teaspoonfuls of the filling 1 to 1 1/2-inches apart along one of the sheets. Brush around filling to moisten then place the remaining pasta sheet over the filling, and press down gently to seal. Be careful to press out any air surrounding the filling. Cut into squares with a pastry wheel. Repeat with remaining dough and filling.
Bring six quarts of water to a boil in a large pot, and add three tablespoons of salt. Drop the ravioli carefully into the pot. Lower the heat, and cook at a brisk simmer until tender, or three to four minutes.
Meanwhile, heat the butter in a large skillet until melted. Add the garlic for about two minutes or until soft then add the mushrooms and cook for another seven minutes, or until soft. Transfer garlic and mushrooms to a bowl, and set aside.
Add sausage to the pan and break it up with a wooden spoon or fork while cooking over medium-high heat. Place the mushroom mixture into the pan with the sausage and mix ingredients well. Slowly sitr the cream and add the Parmesan into the pan over medium-high heat for about two minutes or until thick.
Drain the ravioli and pour into the sausage mushroom sauce and sprinkle with remaining parsley and the Parmigiano Reggiano. Toss for about one minute to coat. Transfer to a platter and serve.