Place dried mushrooms in a small saucepan and cover with hot water; bring to a boil. Cook until tender, about 20 minutes. Drain and chop into small pieces.
Melt butter in a saucepan over medium heat. Add onion; cook and stir until starting to soften, about 3 minutes. Stir in mushrooms; continue cooking until onion is soft, about 5 minutes. Season with salt and black pepper. Add breadcrumbs if filling seems too wet.
Combine flour, hot milk, and egg yolk in a large bowl, stirring quickly with a fork until a soft and smooth dough forms.
Roll dough out on a lightly-floured surface. Cut into 1 1/2-inch squares. Place a teaspoon of filling in the center of each square. Fold the dough over the filling to form a triangle and pinch edges to seal. Bring the bottom corners together and pinch together.
Bring a large pot of lightly salted water to a boil. Cook dumplings in batches until they float to the surface of the water, about 10 minutes. Transfer to a serving plate with a slotted spoon.