Cut the potatoes in cubes and put the potatoes In a saucepan, cover with water, and bring to a boil. Reduce heat and cook on a low boil for about 10 minutes, until the potatoes are tender. Drain potatoes, and let the potatoes cool for at least 15 minutes.
In a Stand mixer bowl with the flat beater paddle and low speed, mix together the Milk , dry yeast and sugar. ( Not Beat) Meanwhile mashed the potato with a fork or potato masher very well.
Add to the yeast mixture the eggs, oil, butter, salt and. the mashed potato, and Beat just until the ingredients mixed.
Now Change the stand mixer flat paddle with the hook dough, and add the flour and turn the mixer to middle high speed and mix for 5 to 6 minutes. If you’re not using the mixer, you’ll need to knead the dough for about 20 minutes. The dough should be smooth, but soft and still a bit tacky feeling. Remove the dough to a light floured hard surface and gentil knead the dough. Shape it into a ball and put it in a greased large bowl.
Cover with piece of plastic wrap. Let rise until doubled in volume, about 40 minutes.
Cut the dough in small ball, 50 grams each piece.
Place the buns on a baking tray lined with a parchment paper.
In a small bowl, whisk together egg yolk and milk.
Using a natural bristle or silicone pastry brush, lightly brush a thin an even layer of egg wash over the buns.
In pre-heated oven temperature 356 F and bake the Buns for about 15 to 20 minutes.
Take the buns from the oven and brush them with melted butter.