Mix the kolache dough: Add all the ingredients except the fruit jam into a mixing bowl with the hook attachment. If your using instant dry yeast, dissolve it with some of the milk and let it stand for about 10 minutes.
Mix the dough on slow speed for 4 minutes, then increase the speed and continue to mix the dough until it’s fully developed, about 6 minutes.
Grease a medium size bowl with some oil and transfer the dough into it, cover with a cloth or plastic, and allow it to ferement for 60 minutes or until it doubles in size.
Divide the Kolache dough: Flour a working surface, then transfer the kolache dough and divide into 12 equal parts, if you have a scale, cut each piece into 57 grams.
Round each divided dough piece into a roll shape and place onto a lined baking sheet with parchament paper. Separate each piece about 3 inches.
Cover and allow to proof in a warm area for about 60 minutes. Pre-heat your oven to 185°C (365°F) about 20 minutes prior to full proof.
Once the kolache dough is proofed, create an indentation in the center of each roll, about 1 inch in diameter and fill it with the fruit jam or fresh fruit.
Repeat until all the rolls are filled.
Egg Wash Glaze: Add the egg and milk into a small bowl and beat together using a whisk.
Brush the top of the kolache with the egg wash.
Place the kolache into the oven and bake for about 16 minutes or until sweet rolls are golden brown.
Remove from the oven and allow kolache pastry rolls to cool before serving.