In a glass measuring cup, combine warm water with yeast and a pinch of sugar. Allow to sit for 5 minutes. While the yeast is proofing, combine the warm milk, sugar, butter, salt, and eggs, and mix well. After the yeast mixture has started bubbling, add it also. Blend in flour, a few cups at a time, until the dough is no longer sticky. Start with the whole wheat flour, adding all of it, then move on to the all-purpose flour, adding just enough to make the dough kneadable (you might not need to use all 5 cups of the all-purpose flour). Knead the dough for 10 minutes on a lightly floured surface. You can also use a stand mixer for everything up to and including the kneading. Lightly oil a large bowl, place dough in it, cover with a towel, and let rise in a warm spot until doubled in size.
When the dough has risen, punch it down, and knead it briefly. On a floured surface, roll dough out to a 1″-thickness. Use a round cookie cutter or biscuit cutter to cut rolls (2½-3 inches). Place rolls, lightly touching, on a buttered cookie sheet, cover with a towel, and let rise 30 more minutes. Bake at 350°F until golden and hollow-sounding when lightly thumped, 20-25 minutes.