“Bloom” the yeast by sprinkling it over the lukewarm water. Let bloom for 5 minutes. You can do the next few steps while you let it bloom.
Place the butter and shortening together in a medium to large microwavable mixing bowl and heat until melted.
Whisk in the warm milk, then whisk in the water and yeast.
Transfer the butter mixture to the bowl of a stand mixer.
Sift in half (3 cups) of the flour. Attach the whisk attachment to your stand mixer and stir the flour until combined.
Add the evaporated milk, sugar, salt, eggs, and egg yolk. Whisk on medium until smooth.
Scrape down the sides of the bowl, the replace the whisk attachment with the dough hook.
Turn the mixer on medium and gradually add the remaining 3 cups of flour. Beat until smooth (2-3 minutes).
Let the dough sit for 5 minutes, then turn the mixer to medium high and beat again until the dough is nice and elastic (about 10-12 minutes).
While the dough is kneading, melt the remaining 5 Tbs of butter in a small bowl.
Remove the bowl from the stand mixer. Brush the top of the dough with melted butter (you will return to the melted butter several times). Cover the bowl with plastic wrap and allow to rise at room temperature for an hour (until the dough has doubled in size).
Punch the dough down, then allow to rise again until doubled (it only takes about half an hour the second time around).
Prepare your baking sheets with parchment paper or silicone baking mats.
Generously flour a clean, flat surface or baking mat, as well as your rolling pin. Keep extra flour on hand.
Dump the proved dough only the floured surface. Roll out into a large rectangle about an inch thick.
Using your biscuit cutter or cookie cutter, cut out circles of dough and transfer them to your prepared baking sheets. Tip: If they become slightly misshapen on transfer, use your biscuit cutter to gently move them back in place.Tip: Cut your dough circles close together in order to re-roll dough out as little as possible.Tip: Place your kolaches about 1/2 inch apart on the baking sheet. They will spread into each other on baking; that’s fine.
Re-roll dough as needed until most of the dough is used up.
Brush melted butter over the top of each circle. Set aside and let prove for 20 minutes.
While the dough is proving the third time, prepare your filling.
For the Apricot Filling
Wash the apricots and remove their stickers (if they have them). Cut them in half and remove the pits.
Add apricots and all other ingredients to a food processor. Process for about 30 seconds
Assembling & Baking Kolaches with Apricot Filling
Once the dough circles have finished proving, use the knuckles of your first two fingers to punch down the center of each circle.
With a spoon, add a heaping tablespoon of filling to the center of each circle.
Let the dough rise another 20-30 minutes.
At the 15-20 minute mark, position one oven rack in the upper third, and one in the lower third. Preheat your oven to 350F.
Bake kolaches until golden brown (about 20-25 minutes).
Brush the warm kolaches with the remaining melted butter. Transfer to wire racks and cool about 30 minutes.