Pour 3 ½ cups all-purpose flour into a mixing bowl. Add 1 ½ teaspoons instant yeast and ¼ cup granulated sugar, and mix them together using a handheld wire whisk.
Heat 1 cup milk to 110–115°F (38°C). Whisk in 2 yolks and ½ teaspoon vanilla extract, then pour the mixture into the flour.
Begin kneading the dough using a stand mixer fitted with a dough hook. Start on low speed and mix for about 1 minute until the ingredients are roughly combined.
After the initial mixing, add ½ teaspoon salt and softened (or slightly melted) ½ stick unsalted butter. Gradually increase the speed to medium-high and knead for 8 minutes, pausing if needed to scrape butter from the sides of the bowl.
Transfer the dough to a clean bowl using the dough scraper. Cover with plastic wrap and let it rise in a warm place until doubled in volume—this usually takes about 1.5 hours, depending on room temperature.
While the dough rises, get the kolache fillings ready.
Once risen, turn the dough out onto a lightly floured surface. Dust the top with flour and fold the edges toward the center. Knead gently to tighten the structure, then place it seam-side down, cover with a towel, and let it rest for 10 minutes.
Divide the dough into equal pieces, each just under 2 oz (50-55 g). Use a kitchen scale if you want evenly sized kolache—this recipe makes about 16.
Take each piece and pull the edges toward the center, sealing the seam with your fingertips. Place seam-side down on a very lightly floured surface and shape into a round using your palm.
Place the shaped balls seam-side down on a parchment-lined baking sheet, leaving about 2 inches (5 cm) between them. Cover with a clean towel and let them rest in a warm place for 30 minutes.
To shape the centers, use a flat-bottomed container wrapped in a clean towel and dipped in flour to prevent sticking. Press down in the center of each dough ball, then press gently around the inner edges to form an even indentation.
Lightly beat 1 egg with a fork and brush the edges of each kolach. This egg wash gives them a beautiful golden shine when baked.
Spoon the fillings into the center. Make sure all fillings are at room temperature.
Preheat the oven to
350 °F using the fan-forced setting. Bake for 14 minutes until the edges turn a nice medium brown. Remove the kolache from the oven and let them cool on a wire rack.