Boil the peeled and diced potatoes in salted water until they are soft (about 15 minutes). Drain and mash them until smooth. Let them cool to room temperature.
In a small bowl, combine the warm milk, sugar, and yeast. Let it sit for 5-10 minutes until the yeast becomes frothy.
In a large bowl, combine the mashed potatoes, melted butter, salt, and the yeast mixture. Gradually add the flour, one cup at a time, stirring until the dough begins to form.
Turn the dough out onto a floured surface and knead for 5-7 minutes until smooth and elastic. If the dough is too sticky, add a little more flour.
Place the dough in a greased bowl, cover it with a kitchen towel, and let it rise in a warm place for about 1 hour, or until doubled in size.
Punch down the dough and divide it into 12 equal portions. Roll each portion into a ball and place them on a greased baking sheet, leaving space between each roll.
Cover the rolls with a kitchen towel and let them rise for another 30-40 minutes, until puffed up.
Preheat your oven to 375°F (190°C). Beat the egg and brush it over the top of each roll for a golden finish.
Bake the rolls in the preheated oven for 15-18 minutes or until golden brown. Remove from the oven and allow them to cool slightly.
In a bowl, combine the cooked chicken, cream cheese, mayonnaise, shredded cheese, mustard (optional), garlic powder, onion powder, salt, and pepper. Mix until smooth and well combined.
Once the potato rolls have cooled a little, carefully slice them in half horizontally, but don’t cut all the way through (like a sandwich bun). Stuff each roll with a generous amount of the chicken filling.
Garnish with fresh parsley or chives if desired. Serve the potato rolls with chicken warm and enjoy!