In a medium sauce pan add the water and the potato and bring them to a boil. Reduce the heat, cover, and simmer for 15 or so minutes or until the potatoes are very tender.
Drain the potatoes but RESERVE 1 cup of the cooking water.
Place the potatoes in a small mixing bowl and mash well. You should have 1 cup of mashed potatoes.
In a small bowl add the cooking water, butter, and salt and stir to combine.
Let the mixture cool until it is about 110 degrees.
In a large mixing bowl or the bowl of your stand mixer add 2 cups of the flour and the yeast.
Add the water mixture to the bowl and stir until well combined.
Add the eggs and mix until well incorporated.
Mix this wet dough on medium to medium high speed for 3 minutes.
Add the mashed potatoes and stir to combine.
Add the flour, 1/4 cup at a time stirring well after each addition, until a smooth dough forms.
Knead the dough by hand (for 6 to 8 minutes) or with your mixer (for 5 minutes) adding any more flour you might need to form a nice dough that is moderately stiff but is still smooth and elastic.
Shape the dough into a ball and place it in a greased bowl, cover with lightly greased plastic wrap (or a beeswax wrap) and let rise until doubled, about an hour.
Turn the dough out onto a lightly floured surface and divide the dough into 2 even pieces.
Cover the dough and let rest for 10 minutes.
Prepare 2 loaf pans (8x4 inches) by greasing them well with butter or shortening (I find that cooking spray doesn't release the bread as well).
Shape each piece of dough into a loaf and place them seam side down into the prepared pans.
Lightly sprinkle the tops with a little flour and place a clean dish towel over the top.
Let rise in a warm place until almost doubled (30 to 40 minutes). I generally let my loaves get 1 inch above the rim of the pan before I bake them.
Preheat the oven to 375 degrees F. and bake the loaves for 35 to 40 minutes or until the bread sounds hollow when tapped lightly.
If they are getting too brown before the cooking time has passed, cover the tops lightly with foil if needed.
Remove from the oven and allow to cool in the pans for 5 minutes before remove them from the pan. Let them finish cooling on a wire rack.
They slice best when they have had time to cool though the warm bread is worth cutting into in my opinion.
Notes
This bread is SO soft and fluffy. It makes the best sandwiches, toast, or eaten warm with butter and honey or jam.
Potato bread can be stored at room temperature either wrapped or in an airtight container for up to 3 days. It can also be frozen, wrapped well, for up to 3 months.
Add flour gradually, mixing well after each addition until you achieve a smooth dough consistency.
Let the dough rise until doubled in size, usually about an hour, then divide and shape into loaves, placing in pans, before allowing them to rise again until about an inch above the sides of the pans.