In a large bowl, combine the eggs and sugar. Mix until all the sugar is incorporated and the color is a light yellow. Add the oil and lemon zest, then stir.
Dissolve the yeast into the warm milk, and add along with the potatoes to the other ingredients in the mixing bowl. Slowly begin to add in all of the flour, scraping the bowl occasionally. The dough should be soft.
Turn out onto a lightly floured board; knead until smooth and elastic, adding flour as needed to keep it from sticking, about 8 minutes. Rub the outside of dough with a small amount of oil to keep moist. Place in a bowl. Cover with a clean dishcloth or plastic wrap; let rise in warm place, free from draft, until doubled in size, about 1 hour. Punch dough down, cover and let rise again until almost double, about 30 minutes.
Punch dough down again; turn out onto lightly floured board. Divide in 6 equal pieces. Roll each piece into a long loaf-shape, about 36 inches long and 1 1/2 inches thick. To make a braided loaf, using two pieces of dough, form a loose braid. Seal the ends of the loaf together with your fingers.
Place the loaves on a baking sheet with parchment paper and cover loosely with a damp towel. Place loaves in a warm place and let rise until doubled in size, about 45 minutes.
Preheat oven to 350˚F. Brush risen loaves with an egg wash (one egg beaten with 1 tablespoon water).
Bake for 50 to 55 minutes, or until golden. Remove from baking sheet and cool on wire racks.