Peel and cut the potatoes into chunks, then put the potatoes into a medium saucepan. The water should cover the potatoes at least an inch. Cook until tender and soft, about 10 minutes.

Drain potatoes and reserve about ⅔ cup water. Mash potatoes and set them aside to cool.

Meanwhile, in a medium microwave-safe bowl, combine milk and ½ cup of the reserved potato water (save the other bit in case the dough is too dry) with the butter pieces, sugar, and salt—microwave for about a minute. Stir until everything melts. If the mixture is too hot, let it cool.

Transfer the mixture to a large bowl, add yeast and eggs, whisk until ingredients are thoroughly mixed, add mashed potatoes and continue mixing.

Next, add the flour a cup at a time. Be careful when adding flour - stop when you can easily form a soft dough ball. It should be slightly sticky. (Too much flour will result in crumby bread or cause the bread not to rise properly - resulting in a dense dough.)

Transfer the dough to a lightly floured surface. Knead for about 6-8 minutes or until the dough is nice and smooth.

Place dough in a greased bowl, turning once to coat the dough. Cover loosely with a clean cloth and let rise in a warm place for 1 ½ to 2 hours or until doubled. Punch the dough down and place it on a clean flat surface or board.

Next, divide the dough into 14-16 pieces, and roll to form even balls (for accuracy, use food scale).

As you roll each ball of dough, place it into a 9x13 greased pan or baking sheet. (Put it on top of a cookie sheet to prevent dough from burning at the bottom.)

Whisk together the egg and milk until thoroughly combined.

Gently brush bread rolls with the egg wash if you want shiny, golden-looking bread rolls, just like in the photos.

Cover with a clean cloth and let rise in a warm place (see notes) for about 20-30 minutes or until doubled.

Bake rolls in a pre-heated oven at 350F/176C for about 15-20 minutes or until golden brown.

Remove rolls from the oven and immediately brush with melted butter. Let them cool slightly before serving.