For the short ribs: Marinate the short ribs with wine, shallot, garlic and herbs overnight.
Preheat the oven at 350 degrees F.
Remove the ribs and keep the marinade for later. Sear the short ribs in a heavy saucepan on medium high or until golden brown on all sides and remove. Add the carrot, leek, celery in the saucepan and caramelize on high heat, then deglaze with the reserved marinade. Bring to a boil and add the short ribs again, veal stock, ketchup, and honey. Season with salt and pepper.
Cover and place in the oven for 3 hours or until the meat falls off the bone. Remove from oven, strain liquid and skim the fat. On medium heat, reduce the braising liquid by half, about 30 minutes. Keep aside for the creamy mushroom sauce.
For the filling: Rehydrate the dried mushrooms in hot water for about 15 minutes and keep the liquid for the sauce.
Place the onions in a saute pan and cook on low heat for about 30 minutes, until golden brown and caramelized, stirring on a regular basis.
In another pan, saute the rehydrated mushrooms in olive oil and season with salt and pepper. Add the shredded short rib meat and caramelized onions. Season with salt and pepper. Keep aside.
For the pasta dough: Place the flour on a table in a mound and make a well in the center. Put the eggs and salt into the well.
Whisk the eggs together with a fork, and gently incorporate the flour into the egg mixture a little at a time. Using your hands, bring the mixture together to form a ball.
Knead the pasta dough, about 5 minutes. Put the dough in a bowl with olive oil. Cover with plastic wrap and let rest for 15 minutes until ready to roll your fresh pasta.
The pasta can be used right away or will keep in the refrigerator for up to a week.
Cut the pasta dough into 4 equal sections. Flatten one of the dough balls with the palm of your hand until it's about 1/2-inch thick and no wider than the slot of the pasta machine. If you don't have a pasta machine, a rolling pin will work fine but make sure to roll the dough thin enough.
Adjust the slot of the pasta machine to its widest setting (usually number 7). Turn the handle while feeding the dough through the slot. Gently hold the flattened dough as it comes out of the pasta machine, but don't pull on it. After the dough has completely passed through the pasta machine, turn the slot down to the next smallest setting and pass the dough through the slot.
As you make the slot smaller, your sheet of dough will become longer. Try to gently hold the dough as it exits the pasta machine so it doesn't tear. Continue passing the dough through the machine until it's about a 1/16-inch thick or number 2 on the pasta machine.
For the ravioli: Using 2 spoons, place about 1 tablespoon of filling into each pocket. Leave 2-inches in between each of them.
Brush the edges of the pasta with water. This will help the ravioli to seal tightly when boiled. Place another sheet of pasta over the ravioli filling. Press out any air to form a seal around each ravioli. Using a cookie cutter to cut desired shape.
Place the raviolis in a single layer on a parchment-lined baking sheet to prevent from sticking. At this point, if you want to freeze the ravioli for later, place the entire baking sheet into the freezer. Once the ravioli have frozen, you can remove the pasta and place them in resealable bags.
For the sauce: In a pan on medium heat, saute the shallots and fresh mushrooms in olive oil and butter until golden brown. Season with salt and pepper. Add reserved short rib braising liquid and water from the rehydrated mushrooms. Continue cooking until quantity is reduced by half, about 15 minutes. Add the cream and let simmer until thickened, about 10 minutes.
For serving: Cook the ravioli in salted boiling water for 2 to 3 minutes or until the ravioli floats. Serve 3 to 4 raviolis per person, add the mushroom sauce and garnish with grated Parmesan cheese and chopped chives.
A pasta machine is great for rolling and cutting the dough. They are inexpensive and can be found at major kitchen stores or online. You can also stuff the ravioli with ground meat or ricotta cheese.