The bread machine makes the dough for the kolache.
In the bread machine's pan, place the water, egg, egg yolk, softened butter, potato flakes, milk powder, salt, sugar, flour and yeast. Be sure you place these ingredients in the pan in the order the manufacturer recommends. Then, select the dough cycle and press start. If necessary, add 1-2 tablespoons of water to the dough after about 5 minutes of mixing.
Once the dough cycle has finished, drop tablespoon-sized dough balls on a lightly greased cookie sheet. The balls should be about the size of walnuts. Cover, wait approximately 1 hour or until dough balls have doubled in size.
Using your hand, slightly flatten the dough balls and use your thumb to make a deeper impression in the center of each dough ball. Take approximately 1 tablespoon of pie filling and fill in the center of each dough ball. Cover, let rise for roughly 30 minutes.
Preheat oven to 375°F.
Bake kolaches for 13-15 minutes, or until slightly browned.
Brush with melted butter immediately after removing from the oven. Cool and serve.