In a small bowl, combine the yeast with a little bit of warm milk and a pinch of sugar. Let it sit for about 10 minutes until it becomes frothy.
In a large mixing bowl, combine the flour, sugar, butter, eggs, salt, and the remaining milk. Mix well until a smooth dough forms.
Add the activated yeast mixture to the dough and knead until well combined. Cover the bowl with a clean kitchen towel and let the dough rise in a warm place for about 1-2 hours, or until it doubles in size.
Once the dough has risen, punch it down to release the air and divide it into small balls.
Flatten each ball into a disk and place a spoonful of fruit preserves or desired filling in the center. Fold the dough over the filling and pinch the edges to seal.
Heat the oil in a deep fryer or large pot to 350°F (180°C). Fry the filled doughnuts in batches until they are golden brown on all sides.
Remove the Pampushky from the oil and drain them on a paper towel to remove excess oil.
Dust the warm Pampushky with powdered sugar before serving.