In a large mixing bowl, whisk together eggs, 11/2 cups water, yeast, dry milk, sugar and oil. Using a stand mixer with a paddle attachment or, if mixing by hand, a wooden spoon, add 3 cups of flour and mix well. Add salt.
Add 1 more cup of flour, then begin kneading with a dough attachment. If by hand, scrape the dough onto a lightly floured counter and, using a bench scraper, reach under the dough, lift it and fold it over itself.
For either method, repeat this motion while gradually adding the remaining 1/2 cup of flour until it's fully incorporated. Resist adding more flour. The dough will be very soft, but easier to handle once it's risen.
Place the dough into a clean bowl coated with cooking spray. Cover with plastic wrap and let rise in a warm, draft-free place until doubled, about 1 to 2 hours.
Turn dough out onto a surface dusted generously with flour. Roll into a rectangle 12 inches wide and 18 inches long. Spread the softened butter evenly over the dough, leaving a 1/2-inch border at the top edge. Sprinkle brown sugar and cinnamon evenly over butter. Working from the widest side, gently roll up the dough into a jellyroll shape as snugly as possible, pinching the border to seal the roll.
Spray a 9-by-13-inch pan, preferably nonstick, with cooking spray. Mark the dough into 12 even pieces, each 11/2 inches wide. Using a 12-inch length of dental floss, work the floss under the dough, then criss-cross the ends and pull, making a clean cut through the dough. Place each roll on its side in the pan. Cover with a cloth and let rise until doubled, about 1 hour.