Whisk flour with salt in a bowl for the dough.

In a separate bowl, beat egg, water, and oil.

Stir the wet ingredients into the flour mixture to form a soft, non-sticky dough.

Add more water, a tablespoon at a time, if needed, being careful not to make the dough sticky.

Turn the dough onto a lightly floured surface and knead until smooth, about 5 minutes.

Divide the dough in half.

Cover with plastic wrap or a damp tea towel and let rest for 20 minutes.

For the mushroom filling, cover dried mushrooms with boiling water in a heatproof bowl.

Let stand until softened, about 20 minutes.

Drain and finely chop the soaked mushrooms.

Melt butter in a skillet over medium heat.

Cook soaked and fresh mushrooms and minced onion, stirring often, until tender and liquid has evaporated, about 8 minutes.

Remove from heat and let cool slightly.

Stir in dill, egg yolk, salt, and pepper.

Working with half of the dough at a time and keeping the remainder covered, roll out on a lightly floured surface to about 1/16-inch thickness.

Cut out rounds with a 3-inch round cookie cutter.

Place 1 teaspoon of the filling on the center of each round.

Lightly moisten the edge of half of each round with water.

Fold in half and pinch edges together to seal and crimp attractively.

Place on tea towel-lined rimmed baking sheets and cover with a damp towel to prevent drying out.

Repeat with remaining dough and filling.

Refrigerate for up to 8 hours if making ahead.

Cook perogies in batches in a large pot of boiling salted water, stirring gently to prevent sticking, until they float to the top, about 2 minutes.

Transfer to a colander to drain.

Melt butter in a large skillet over medium heat.

Cook sliced onion until golden, about 5 minutes.

Add perogies and toss to coat and warm through.

Serve with sour cream.