In a large bowl, combine flour, baking powder and salt. Make a well in the centre and pour water, oil and egg. Mix with a fork or with your hands. Place dough on a lightly floured work surface and knead until smooth. Form into a disc with your hands. Cover with plastic wrap and refrigerate for 30 minutes.
In a bowl, combine mashed potatoes, cheese and chives. Season with salt and pepper. Set aside.
On a floured work surface, roll out dough into a 2-mm thick sheet. With a 7.5-cm (3-inch) round cookie cutter, cut 24 discs. Place about 10 ml (2 teaspoons) of filling in the centre of each disc. Brush edges with water and close into half-moons, pressing edges to seal. Set aside on a lightly floured baking sheet.
In a large pot of salted boiling water, cook pierogis until al dente (until they rise to the surface of the water, about 4 minutes of cooking). Drain and place on a lightly oiled baking sheet.
In a non-stick skillet, brown shallots in butter. Add pierogis and brown on both sides. Add butter, if needed. Season with salt and pepper. Serve with sour cream. If desired, serve with Pozharsky Veal Croquettes (see recipe).