Preheat oven to 350 degrees F.
In a small bowl, add the warm water, yeast, and sugar and mix to combine. Let sit for about 5-10 minutes, or until the yeast mixture starts to get bubbly.
Meanwhile, add the milk to a small pot and bring to a boil. Remove from heat.
In the bowl of a stand mixer add the scalded milk, mashed potatoes, soft butter, and salt and mix on low until combined using the dough hook. Let the mixture sit until it becomes lukewarm, then add the yeast mixture and eggs.
Add half of the flour and mix on low until combined. Stir in the remaining flour, ½ cup at a time until the dough starts to pull away from the sides of the bowl as it mixes. Allow the dough to mix on medium for about 3 minutes once the flour has been added.
Turn the mixer off, cover the bowl loosely with a kitchen towel or plastic wrap and let the dough rise until light and puffy, or about 30-45 minutes.
Once the dough has doubled in size, transfer to a lightly floured surface and divide into 24 equal pieces. Roll each piece into a ball and place into 1-2 greased baking dishes, spacing them out evenly so that they are almost touching.
Cover loosely and let the rolls rise in a warm place for about 30 minutes, or until doubled in size.
Bake in your preheated oven for 15-18 minutes, or until the rolls are golden brown on top.
Remove from the oven and let cool for 1-2 minutes, then brush the tops with melted butter. Enjoy!