To make the dough in an electric stand mixer: 

1. In a small bowl lightly whisk 1 whole egg, both egg yolks and the lukewarm milk.
2. Place the egg mixture, flour, salt, powdered sugar and yeast in the bowl of an electric stand mixer, and using the dough hook, mix for 1 minute.
3. Add the butter, and mix until the dough is shiny and smooth, about 7 minutes.
4. With your hands, form the dough into a smooth, round ball.

To make the dough by hand:

1. In a large bowl mix together the flour, salt, powdered sugar, and yeast.
2. In a small bowl lightly whisk 1 whole egg, 2 egg yolks, and lukewarm milk.
3. Add the egg mixture to the flour mixture, and mix to combine with a wooden spoon. Add the butter. (It’s probably going to be too hard to stir and incorporate thoroughly with a wooden spoon, so feel free to dump the dough on a clean, lightly floured surface, and mix with your hands).
4. Toss, turn and knead the dough with the palm of your hands for 7 minutes, until glossy and elastic.
5. With your hands, form the dough into a smooth, round ball.

Once you have your dough:

1. Grease the bottom and sides of a large bowl with the vegetable oil. Place the dough in the bowl and cover it with a clean kitchen towel.
2. Let the dough rise undisturbed, in a warm place, until doubled in size, about 50 min – 1½ hours

While the dough is rising: 

1. Make the streusel topping: In a small bowl, combine the flour and sugar. Work in the butter with your fingers, lightly toss and mix, until crumbled and pea-size.
2. In a bowl, lightly beat the 1 egg you reserved for brushing the dough.

To form kolache:

1. Preheat the oven to 350°F (180°C), place two oven racks in the middle of the oven, and line four baking sheets with parchment paper.
2. Dump the dough onto a lightly floured surface and divide into 4 equal parts.
3. Shape each part into a bun and place it in the middle of a baking sheet. With your hands, gently flatten and tap the dough into a circle about 10 inches in diameter, ¼ inch high, and with a ¾-inch wide edge.
4. Arrange the fruit evenly on top of the dough (strawberries and apricots cut-side down). Use either one type of fruit per koláč, or combine two or all three in a fun circular pattern.
5. Brush the edge with the egg. Sprinkle 1/3 cup of the streusel evenly over the fruit, and lightly press down.
6. Bake the koláče—two at a time—in the oven until the edge is golden brown, about 20–25 minutes. For even baking, switch the baking sheets halfway through, placing the top one on bottom and vice versa.
7. Transfer to a cooling rack and let cool for about 45 minutes. Cut into slices and serve.