Warm about 200 ml of Whole Milk until just lukewarm, stir in Sugar and sprinkle over Instant Yeast; let sit 5–10 minutes until foamy.
Into a large bowl whisk one beaten Eggs, the foamed yeast mixture, melted Unsalted Butter and a pinch of Fine Salt. Gradually add All-Purpose Flour and knead until you have a soft, smooth dough. Cover and let rise in a warm place until doubled, about 1–1½ hours.
While the dough rises, cook the White Rice according to package instructions and cool to room temperature.
In a skillet melt more Unsalted Butter and sauté chopped Onions until translucent, then add chopped Mushrooms and cook until their moisture has evaporated and they are golden; season with Salt and Black Pepper. Stir in chopped Fresh Dill and let the mixture cool.
Season the Salmon Fillet with a little Salt and Black Pepper, then pan-sear or bake until just cooked through. Let cool slightly and flake into large pieces.
Combine the cooked rice with the mushroom–onion–dill mixture and gently fold in the flaked salmon, tasting and adjusting seasoning as needed.
On a lightly floured surface (dust with Flour) roll the risen dough into a large rectangle about 1/4-inch thick. Sprinkle a thin layer of Plain Breadcrumbs along the center strip of the dough to absorb excess moisture.
Mound half of the rice–salmon filling down the center, optionally add some larger salmon pieces for a visible layer, then top with the remaining filling. Fold the long sides of the dough up and over the filling to enclose, pinching and sealing the seams; tuck the ends under to form a neat loaf.
Place the seam-side down on a baking sheet. Beat the remaining egg with Milk to make an egg wash and brush the surface; let the assembled pie rest 10–15 minutes, score a few slits for steam to escape and add decorative dough trims if you like.
Preheat the oven to 190°C (375°F) and bake the kulebyaka for 35–45 minutes, until deeply golden and cooked through.
When the pie is hot from the oven, brush the crust with melted Butter. Let the kulebyaka rest 15 minutes before slicing so the layers settle—serve warm or at room temperature.
