This Russian dish has many variations all around the Baltic. This recipe is the one most common to Finland. In fact, it could be considered a Finnish national dish. Serve with a green salad along with a sour cream and dill dressing.
Sift the flour, yeast and salt into a bowl and make a well in the center. (If using fresh yeast, mix this with a little warm milk and a pinch of sugar and set aside for 10 minutes until it becomes active and frothing).
Scald the milk and butter, then let them cool to blood temperature. Mix the sour cream, whole eggs, egg yolks together throughly then add to the well along with the lukewarm milk.
With a wooden spoon, gradually incorporate the liquids into the flour mixture.
Once the mixture is combined into a ball, knead vigorously for 10 minutes until the dough is elastic.
Put the dough into a greased bowl, cover it and set it aside to allow it to raise to double the original volume (about 1.5 hours). When it has risen, punch it down and knead it briefly.
Divide the dough into two equal halves, wrap them, and place into the refrigerator to chill until you are ready to assemble the dish.
In a large frying pan, cook the salmon fillet in butter for two minutes on each side. Set aside, season it and sprinkle with half of the lemon juice. Chill until ready to use.
Cook the onions in the remaining butter until they become translucent. Add the mushrooms and a pinch of salt. Cover and cook until the juices run. Remove the lid, turn up the heat, and quickly evaporate the juices.
Place the onion and mushrooms in to a mixing bowl along with the remaining lemon juice. Toss to coat everything then add cooked rice, raw egg, herbs, spices and seasonings, and mix together everything well in the bowl.
On a floured board, toss out one dough half.and roll out to an oblong 1/3 inch thick, which will fit your baking sheet. Place on a baking sheet and spoon onto it the rice mixture, leaving a rim about 1 1/2 inches wide.
Arrange the salmon on top of the rice and slices of egg on top of the salmon. Cover with the remaining rice mixture.
Dampen the edges of the dough with water. Roll out the second piece of dough to the same size as the first and place over the filling. Press together the edges firmly. Turn them up and then press them together again using the tines of a fork.
Make a small steam hole in the top center of the pie, and, if you have extra dough left, feel free to decorate the pie with leaves and braids.
Brush the pie all over with the sour cream and bake in a preheated oven at 400F for 45-60 minutes, until the pastry is golden brown. Place the pie on a serving platter and pour the melted butter into the hole on top. Serve hot.