- For the dough, put all of the ingredients in the bowl of a mixer fitted with the dough hook attachment and mix on low speed until blended, increasing the speed to medium to knead until the dough feels elastic, about five minutes. Alternatively, the dough can be mixed by hand, and turned onto a work surface to be kneaded until elastic (7-10 minutes). Place the dough in a bowl, cover and allow to rise until doubled, about an hour.
- While the dough is rising, prepare the filling. Boil the potatoes in salted water until tender and drain. Use a mixer, beaters or a ricer to mash the potatoes and stir in the butter and cheese. Season to taste and cool to room temperature (this can be prepared a day ahead and chilled).
- Turn the risen dough out onto lightly floured work surface, divide into two pieces and roll out each piece into a large oval, about ½-inch thick. Divide the filling between the two pieces of dough and spread it to cover half of each piece of the dough. Fold the unfilled half over the filling (the bread should now have a giant pierogy shape to it), press out any air pockets and pinch the edges closed. Place the breads onto parchment-lined baking trays, cover each with a tea towel and let rise for 30 minutes.
- Preheat the oven to 375°F. Use a fork to dock the top of the bread a little and brush with the egg wash. Bake the bread for about 40 minutes, until golden brown. Cool for at least 15 minutes before slicing to serve.
The bread will keep for up to two days, well-wrapped or can be frozen.