In a medium bowl, combine the warm water, sugar, and yeast. Let it sit for 5-10 minutes until the yeast bubbles and is foamy on top.
In a large bowl of a stand mixer fitted with a paddle attachment, combine the proofed yeast with the mashed potatoes, milk, eggs, butter, salt, and 2 cups of flour. Beat until combined, about 1 minute.
Switch the paddle attachment for the dough hook and begin to knead the dough on medium-low speed, adding additional flour 1 cup at a time until incorporated to make a soft, slightly sticky dough. Knead on medium-low speed for 6-8 minutes until smooth.
Transfer to a clean bowl that has been lightly greased with 1-2 teaspoons of oil oiled. Cover with plastic wrap or a clean cloth, then let the dough rise in a warm spot for 60-90 minutes until doubled in size.
When the dough has risen, make a fist and punch the dough down right in the center to let out air. Pinch the dough in half and shape into 2 loaves by shaping into oblong balls. Place each ball of dough into a bread pan that has been sprayed with cooking spray.
Cover loaves again with plastic wrap or a clean cloth and let them rise for another 30-60 minutes.
Preheat oven to 350°F. Just before baking, brush the tops of each loaf with a little water using a pastry brush and sprinkle with a little flour for decoration.
Bake at 350°F for 35-40 minutes until golden brown on top.
Let cool in the loaf pans for 5-10 minutes before turning out onto a wire rack to finish cooling. Store in an airtight container.