Warm the milk on the stove or in the microwave until lukewarm. Add the poppy seeds, cover and let sit for at least 2 hours.
In a heavy-bottomed pot or over a double boiler, whisk together the sugar and cornstarch to remove any lumps. Then add the poppy seeds and the milk they were soaked in, as well as the eggs.
Cook over low heat, stirring constantly, until thickened, about 10-15 minutes. Remove from the heat and add the butter, vanilla and salt and stir until combined and the butter melts in.
Transfer to a bowl or a sheet pan, and cover with plastic wrap to prevent a skin from forming. Chill in the refrigerator until completely cool.
Combine the tangzhong ingredients in a small saucepan set over medium heat. Whisk and heat until it becomes a thick paste. Remove from heat and set aside to cool.
In the bowl of a stand mixer or in a large bowl, thoroughly whisk together 2 cups of the flour, the instant yeast, sugar, salt and diastatic malt powder, if using.
Warm the milk to 100-110°F. Add the paddle attachment to the mixer and stream in the warm milk while mixing on the lowest setting. When combined, turn the mixer off and let sit for 5-10 minutes to activate the yeast.
Add the tangzhong, oil, butter and egg and the rest of the flour. Switch to the dough hook. Continue mixing. If the dough looks too wet and sticks to the sides of the bowl, add more flour 1 tablespoon at a time.
Mix with the dough hook on medium speed for 6-8 minutes. When the dough starts looking smooth, conduct the windowpane test.
When the dough passes the test, transfer to a large greased bowl and cover. Let rise until doubled, about 1 hour.
Whisk together flour, sugar and salt. Cut butter into dry whisked ingredients with a pastry blender or two knives until you have a fine crumb. Set aside.
Punch down the dough after rising. Pinch off egg-size sections of dough and roll into balls. Place 20 balls per sheet in 4 rows of 5 on a greased baking sheet. Cover and let rise for 30 minutes.
Preheat the oven to 375°F. Firmly press down the centers of each kolache with thumbs or a tamper.
Fill the divots with about 2 tablespoons of the cooled poppy seed filling. Sprinkle with posipka, if desired, or leave plain to add icing later. Cover with an inverted baking sheet and proof for 20 minutes.
Bake for 15-18 minutes or until lightly golden in color. Brush edges with melted butter after baking, if desired.
To make the glaze (optional): Add half of the lemon juice to the powdered sugar and whisk. Use more, as needed, to get your desired consistency. Drizzle over cooled kolaches.
