In a large saute pan heat 1/4 cup of the olive oil. When almost smoking, add the mushrooms and season with salt and pepper. Cook until all the liquid has evaporated from the mushrooms, about 6 minutes. Remove from heat and place mixture into the bowl of a food processor. Pulse until you get a coarse texture. Place in bowl and stir in ricotta and Parmesan cheese. Check for seasoning and set aside.
Line up 3 wrappers on a cutting board. Brush with the egg and water mixture. Using a tablespoon, arrange 4 dollops of the filling on each wrapper – 2 on the first row and 2 on the second – 1-inch apart. Place another wrapper directly on top, pressing around the filling and sealing the edges. Using a fluted ravioli cutter, cut out squares of ravioli. Each filled wrapper will yield 4 raviolis, giving you a total of 12 ravioli. Place ravioli onto a floured baking sheet and keep covered with a linen towel.
In a large pot, bring to a boil 4 quarts of salted and oiled water. Carefully add small batches of ravioli, about 3 to 4 at a time. This will prevent them from crowding in the pot and sticking together. Cook for 2 to 3 minutes. Using a spider strainer, carefully remove the ravioli and place on the plate. Tent with foil to keep warm and continue cooking remaining ravioli.
In a saute pan, heat remaining 1/4 cup olive oil. When almost smoking, add chopped kale and saute until soft and most of the liquid has evaporated, about 8 minutes and add fresh wants. Divide ravioli between 2 serving plates. Top with shaved Parmiggiano.