How to Make It
In a small bowl, stir the yeast and 1/2 teaspoon of the sugar into the warm milk. Let stand until foamy, about 5 minutes.
In a large bowl, whisk the 1 1/2 cups of all-purpose flour with the buckwheat flour, salt and the remaining 1 tablespoon of sugar. Stir in the yeast mixture, beaten egg and melted butter and knead until a smooth dough forms. Transfer the dough to a lightly oiled bowl, cover with plastic wrap and let stand in a warm place until doubled in volume, about 1 1/4 hours. Punch down the dough, cover and let rise again until doubled, about 1 1/4 hours longer.
In a medium saucepan, cover the potato chunks with water and bring to a boil. Add a large pinch of salt and cook over moderately high heat until tender, about 8 minutes. Drain the potato and return the chunks to the pan, shaking over the heat to dry them out, about 10 seconds. Pass the warm potatoes through a ricer into a large bowl or mash them with a potato masher.
In a medium skillet, heat the 2 tablespoons of oil. Add the leek and a pinch of salt and cook over moderate heat, stirring occasionally, until softened, about 6 minutes. Remove from the heat and stir in the butter. Add the leek to the potatoes along with the cream cheese and heavy cream, stir well and season with salt and pepper.
Punch down the dough again. Transfer to a lightly floured work surface and shape it into a rectangle. Roll the dough out into a 8-by-20-inch rectangle, about 1/8 inch thick. Cut the dough into eight 4-by-5-inch rectangles. Set 1 rectangle with a long side toward you and spoon 1/4 cup of the potato filling on the top third; leave a 1/3-inch border on the top and sides. Bring the bottom of the dough up and over the filling, fold all the sides over themselves and press to seal. Repeat to form the remaining knishes. Brush the knishes with the beaten egg, coating the seams well. Place the knishes on a parchment paper–lined baking sheet and freeze for 10 minutes.
Preheat the oven to 350°. In a medium saucepan, heat 1 1/2 inches of vegetable oil to 375°. Set a wire rack over a rimmed baking sheet near the stove. Fry 2 knishes at a time, turning them a few times, until richly browned, about 2 minutes. Using a slotted spoon, transfer the knishes to the rack to drain. Keep the fried knishes hot in the oven.
Cut the knishes on the diagonal into 2 1/2-inch pieces. Top with sour cream, dill, red onion and caviar and serve right away.
The knish filling can be refrigerated overnight. Bring to room temperature before proceeding.