Prepare the dough:

1. In a medium mixing bowl, whisk to combine milk, sugar, yeast, eggs, and butter until smooth. Set aside for 5 minutes until bubbles form on top.
2. In a large mixing bowl, stir together flour, mashed potatoes, and salt until evenly combined.
3. Slowly pour the wet mixture into the flour mixture. Mix well until it forms a shaggy dough, scraping down the sides of the bowl (there should be no dry flour particles visible).
4. Knead the dough for 8-10 minutes until a smooth and soft dough ball is formed. You can also knead the dough on medium speed in a stand mixer for 8-10 minutes until smooth dough ball is formed.
5. Cover the bowl and let the dough rise until doubled in size, about 1 hour. You can lightly oil the dough ball to prevent sticking.

Shape the rolls:

1. Roll the dough into a log and use a bench scraper to divide it into 15 equal pieces. Cover the dough with a damp cloth or plastic cling wrap to prevent it from drying. Take one piece at a time and shape each piece into a smooth ball. Use the palms of your hands to flatten each dough, then fold and press all edges into the centre. Turn it over and cup the dough in the palm of your hand, making circular motions until you create a ball. It should take less than 30 seconds to roll each piece into a smooth ball.
2. Arrange the dough balls into a 9x13-inch casserole pan, spacing them evenly into 5 rows and 3 columns.
3. Cover the pan loosely with plastic cling wrap and let the rolls rise until almost doubled in size, about 45 minutes.

Bake the rolls:

1. Preheat oven to 350 F.
2. Bake the potato dinner rolls for 22-25 minutes until golden brown.
3. Brush the top with some melted butter (if desired) and let the rolls cool on a wire rack for 15 minutes before serving.