To make the dough, in a large bowl, combine the yeast, warm milk, sugar, and 1 cup of the flour. Cover and let it rise until doubled in size.
Beat together the eggs, 1/2 cup of melted butter (reserve 1/4 cup for brushing on the pastry), and salt. Add the egg mixture to the yeast mixture and blend.
Stir in about 2 more cups of flour, 1/2 cup at a time. The dough should be soft and moist. Knead dough for about 10 minutes on floured surface. Don’t worry, it’s a joy to knead as the dough is smooth and highly malleable. Put dough in a greased bowl and let rise covered until doubled in size—about an hour.
After dough has risen, punch it down and pull off egg-sized pieces. In your hands, roll pieces into balls and then flatten to about 3 inches in diameter. Brush with half the remaining melted butter. Place flattened pieces on a greased cookie sheet, cover ,and let rise again for another half-hour.
Meanwhile, to make the filing, place the fruit in a pan, cover with water, bring to a boil, then cook on low for 15 minutes, adding sugar to taste (I find the fruit sweet enough so I don’t add sugar, but you may prefer it sweeter), cinnamon, and lemon zest. Mash with a potato masher until you have a puree.
To make the popsyka, stir together the flour, sugar, butter, and cinnamon until crumbly.
After the second rising of the dough, with your finger gently make an indention in the center of the dough (be careful not to flatten it too much) and fill with one tablespoon of fruit filling and sprinkle with the posypka.
Bake in oven at 375° F for 12 to 15 minutes. Brush with remaining melted butter when you take them out of the oven and serve warm.
Notes
For additional flavor you can soak the dried fruit in tea such as Earl Grey or you could sprinkle goat cheese on the apricot kolaches before baking. You can also make sausage and jalapeno kolaches, which are officially known as klobasniky, by wrapping the three-inch flattened piece of dough around a two-inch piece of sausage and a couple of pickled jalapeno slices.