Preheat the oven to 400°. Prick the potatoes all over and bake for about 45 minutes, or until tender. Let cool completely, then peel the potatoes and pass them through a ricer or finely mash them. Measure out 3 1/2 cups of potatoes.
In a very large bowl, stir the yeast into 2 cups of the lukewarm water and let stand for about 5 minutes, or until the yeast is foamy. In another large bowl, combine 6 1/2 cups of the flour, the dry milk powder, sugar, dill and salt with half of the caraway seeds. Using your hands, work the 3 1/2 cups of riced potatoes into the flour mixture. Add the potato mixture and the beaten eggs to the dissolved yeast and mix vigorously until a soft, lumpy dough forms.
Scrape the dough out onto a lightly floured work surface and knead in up to 1 1/2 cups more flour to make a smooth, satiny dough that is just slightly sticky. Put the dough in a large, lightly buttered bowl, cover with plastic wrap and set aside in a warm place until doubled in volume, about 45 minutes.
Butter 2 large baking sheets. Punch down the dough and knead it briefly. Cut the dough into 24 even pieces and shape each piece into a ball. On 1 baking sheet, arrange half of the dough balls in 2 rows of 6, with the pieces lightly touching each other. Repeat with the remaining dough balls on the second sheet. In a small bowl, beat the remaining egg with the remaining 1 tablespoon of water. Brush the tops of the loaves all over with the egg wash, then sprinkle on the remaining caraway seeds. Let the loaves stand in a warm place until doubled in volume, about 40 minutes.
Preheat the oven to 375°. Bake the loaves for about 30 minutes, covering them with foil after the first 5 minutes to prevent the tops from burning; rotate the pans halfway through baking. When the tops of the loaves are lightly golden, remove the foil and bake for about 8 minutes longer, or until the loaves are evenly browned. Transfer the loaves to racks to cool. Serve warm or at room temperature.
The bread can be baked 1 day ahead; wrap well and let stand at room temperature. Before serving, wrap the bread in foil and rewarm in a 350° oven.