"Great recipe for traditional Polish pierogi filled with sauerkraut and dried mushrooms. Packed full of flavor and delicious, they taste best drizzled with melted butter, caramelized onions, and sour cream."
Combine 1 cup water and dried mushrooms in a saucepan over low heat, bring to a simmer, and cook until tender, about 10 minutes. Drain mushrooms, reserving cooking water. Chop mushrooms.
Heat olive oil in a separate saucepan over medium heat and cook onion until soft and translucent, about 5 minutes. Add mushrooms and sauerkraut and mix well; season with salt and pepper. Pour in the cooking water, cover, and simmer until water has evaporated and sauerkraut is soft, 15 to 20 minutes.
Place flour in a large bowl and make a well in the center. Crack egg into the well and add enough warm water, 1 tablespoon at a time, until a dough forms, stirring constantly with your hands. Knead well, continuing to add more water as needed. Knead until dough is soft and smooth.
Dust a work surface with flour. Cut off 1/4 of the dough and roll out to a thickness of 1/8 inch. Cut out circles using a glass or a round pastry cutter.
Fill each dough circle with 1 teaspoon of sauerkraut filling. Fold dough over into a half-moon shape and seal edges. Cover with a clean dish towel so pierogi won't dry out and repeat with remaining dough and filling.
Bring a large pan of salted water to a gentle boil. Add the pierogi in batches and cook until they float to the surface, 5 to 7 minutes. Cook for 2 to 3 minutes once they float to the surface. Remove with a slotted spoon and drizzle with melted butter.