Put 2 ½ cups all-purpose flour, ¾ cup lukewarm milk, 2 egg yolks, ⅓ cup granulated sugar, and 1 ½ teaspoons instant yeast in a mixing bowl. In a stand mixer fitted with the kneading hook, mix briefly, just one minute on speed two. Turn off the mixer, and add 6 Tablespoons sunflower oil and ¼ teaspoon salt. Continue to knead on medium speed for about 8 minutes.
Turn the dough out onto a lightly floured work surface and form into a ball. The dough should be smooth and pliable. Transfer the ball of dough to a clean bowl, cover with a tea towel or plastic wrap, and let rise in a warm place until doubled in size.
Make poppy seed filling: Combine 3 cups ground poppy seeds, ¾ cup granulated sugar, and 1 ¼ cup milk in a saucepan. Bring to a boil, stirring constantly. Reduce the heat to one-third and simmer for about five minutes. Finally, stir in 1 Tablespoon lemon zest and 2 Tablespoons jam. Set aside to cool to room temperature.
Briefly knead the dough with your hands. Divide the dough into equally-sized pieces; if you are using the basic recipe amount (found in the recipe card below), divide the dough into 12 pieces.
Fold the edges of each piece of dough toward the center and firmly seal them. Shape the dough into small balls, working it gently. Put the dough balls on a lightly floured surface, ensuring the seam side is facing down. Allow them to rise for approximately 20 minutes (the so-called second rise).
Prepare a baking sheet by lining it with parchment paper. Then, arrange the proofed dough balls on the sheet, ensuring there's ample space between each one, at least 2 ½ inches apart.
Next, create an indentation in the center of the kolaches. Grab a round container with a smooth bottom. Wrap the container's base with a clean cloth and lightly dip it in flour.
Using the prepared container, press down on the center of the dough, causing the edges to enclose it. You may need to use some force, especially as the kolach center should be thin.
After pressing the kolache in the middle, brush their edges with the beaten egg. This egg wash will give the edges a golden and shiny appearance once they are baked.
Generously fill the centers of the kolache with poppy seed filling. The filling should be at room temperature.
Enhance the kolache by sprinkling the surface with Posypka, a crumble mixture of butter, flour, and sugar. For the Posypka streusel topping, mix with your fingers 2 Tablespoons unsalted butter, 2 Tablespoons granulated sugar, and 3 Tablespoons all-purpose flour in a bowl until fine to coarse crumbs form. Alternatively, consider placing a blanched almond in the center of the poppyseed filling.
Preheat the oven to
350 °F. Place the sheet of kolache in the oven and bake for 20 minutes. The edges will be golden brown. Transfer the baking sheet with baked kolaches to a wire rack and allow to cool.