Stir1 teaspoon granulated sugar and the 2 teaspoons active dry yeast into ½ cup of the lukewarm milk (110–115°F / 38°C). Let the mixture sit in a warm place for about 10–15 minutes, until a bubbly foam forms on the surface.
In a large bowl, combine 4 cups all-purpose flour with 1 egg, ½ teaspoon salt, the activated yeast mixture and the rest of milk. Mix everything with a spoon first, then transfer the dough to a work surface and knead by hand until soft and smooth. Alternatively, you can use a stand mixer fitted with a dough hook to make this step easier.
Shape the dough into a ball and place it in a bowl. Cover with plastic wrap or a clean kitchen towel, and let it rise in a warm place until doubled in size. This usually takes between 45 minutes and 1½ hours, depending on the room temperature.
While the dough is rising, mix 1 teaspoon granulated sugar with the clean, drained 2 cups blueberries.
Once the dough has risen, roll it out into a smooth rectangle about as thick as a drinking straw (not too thin). Cut it into squares, each roughly 3 inches on each side. Place a scant tablespoon of the sweetened blueberries in the center of each square. Carefully fold the edges of the dough over the filling and pinch the seams well to seal.
Bring a large saucepan of lightly salted water to a full boil. Reduce the heat to medium, then gently place the dumplings into the water. Cover with a lid and cook for 8 minutes without flipping them.
When the dumplings are done, remove them with a slotted spoon and transfer to a bowl. Immediately prick each one with a fork to release the steam. If you are not serving them right away, brush the tops with melted butter to keep them from drying out.
Serve the dumplings warm, topped with crumbled farmer’s cheese, a dusting of powdered sugar, and a generous drizzle of melted butter.