How to Make It
Heat the olive oil in a large skillet. Add the mushrooms and cook over low heat until the liquid they release has evaporated, about 5 minutes. Add the shallot and cook, stirring, until softened and the mushrooms are lightly browned, about 5 minutes. Transfer the mushrooms to a cutting board and let cool, then finely chop.
In a medium bowl, mix the mushrooms with the egg yolk, parsley and 3 tablespoons of Parmesan. Season with salt and pepper.
Lay 4 wonton wrappers on a work surface and moisten the edges with water. Mound 1 1/2 teaspoons of the mushroom filling just below the center of each wrapper. Bring 2 opposite corners together over the filling to form a triangle. Press all around the filling to release any air pockets and seal the dumplings. Moisten the opposite tips, bring them together and press to seal. Repeat with the remaining wrappers and filling.
Bring a large saucepan of water to a boil. Add salt and the dumplings and cook until just tender, about 1 1/2 minutes. Drain and transfer to shallow bowls. Pour the hot stock over the dumplings, sprinkle with Parmesan and serve.