Peel and boil about 6 small potatoes in salted water in a small saucepan. In the meantime, measure the milk, margarine, sugar and salt together. When the potatoes have cooked through, drain them and mash in the milk mixture. Transfer into a food processor and pulse until smooth. By now, the mixture should have cooled to about 110 degrees. Sprinkle in the yeast and let rest for 10 minutes.
Place the flour in the bowl of a stand mixer and attach the dough hook. Pour in the potato mixture and run the mixer for 10 minutes. Coat the dough ball with half of the olive oil and roll it around in the bowl. Cover the bowl with a moist cloth and let rise in a warm place for about 30 minutes or until doubled.
Using a floured surface, knead the dough about a dozen times; coat it with the remaining olive oil and return it to the bowl. Cover with the moist cloth and let it rise again in a warm place for about 30 minutes or until doubled.
Use cooking spray to coat two loaf pans. Punch the dough down, form it into two separate loaves and set it into the pans. Cover it and let it rise one final time in the warm place for about 15 minutes. Preheat the oven to 375 degrees.
Mix the honey and water together and brush it over the surface of the loaves. Bake for approximately 30 minutes or until a rich golden brown, and hollow sounding when tapped. Cool for 5 minutes, then remove from pans to cool completely.