Add the flour, powdered sugar, cocoa powder, and salt to a large mixing bowl and stir them together.
In a small saucepan, warm the water with butter until they are very warm but not boiling (temperature should be around 176°F/80°C, that is when the water starts to move and steam).
Pour hot water with butter into the bowl with flour, and mix with a wooden spoon until roughly combined.
Knead the dough by hand or using a stand mixer fitted with a dough hook for about 5 minutes. You can also use a food processor with a dough blade. The dough should be smooth, soft, and not sticky—it will become even softer after resting. If you follow the recipe closely, especially if you weigh the ingredients instead of using measuring cups, the dough should turn out just right. However, if it feels too dry, add a little water; if it’s too wet, add a bit of flour until you reach the perfect consistency.
Wrap the dough in plastic foil and leave to rest for about 40 minutes (don’t omit this step).
In the meantime, you can wash the fruit and pat it dry with paper towels but don’t prepare the filling just yet – the sugar will start extracting water from the fruit, the fruit will get watery, and it will be difficult to stuff pierogi with watery filling!