Mushroom Ravioli with Fresh Pasta

Ingredients

• 2 whole eggs
• 2 egg yolks
• 1 Tbsp oil
• 2 Tbsp water
• Kosher salt
• 1 3/4 cup flour
• 1 oz (28 g) dried assorted wild mushrooms such as chanterelle, porcini, black trumpet, cauliflower, pine and lobster mushrooms (often sold in ½ ounce packets)
• 2 Tbsp vegetable oil
• 3/4 cup finely diced shallots, about 2 shallots
• 2 garlic cloves, finely chopped
• 3 cups finely chopped cleaned crimini or white button mushrooms, about 3/4 pound
• Zest from one washed lemon
• 1 Tbsp freshly squeezed lemon juice
• 1/4 cup freshly grated Reggiano Parmesan
• 1/4 cup goat cheese
• 2 Tbsp freshly chopped thyme
• 1 Tbsp freshly chopped parsley
• Mushroom liquid from the dried mushrooms
• 4 Tbsp vegetable oil, plus more as needed
• 3 cups sliced fresh mushrooms, about 3/4 pounds
• 3/4 cup dry white wine
• 1 1/2 cups whipping cream
• 1/2 cup freshly grated Reggiano Parmesan
• 1 tsp freshly squeezed lemon juice