For the Dough:
Heat milk, sugar and salt in saucepan over medium-high heat. Stir until sugar melts and a few small bubbles appear at the edges of pan. Remove from heat and let cool while you prepare the other elements.
Dissolve yeast and 1 teaspoon sugar in warm water (90°F to 110°F) in bowl of stand mixer. Stir mixture with paddle attachment (or wooden spoon) until well-blended. Let stand 10 minutes.
Beat eggs into yeast mixture. Stir in cooled milk mixture (it should be lukewarm, 98°F to 115°F) and switch to dough hook. Add in flour a little at a time until dough is elastic. Add melted butter and mix again; add in more flour until dough is elastic and pulls away from sides of mixer. You may not have to use all the flour: do not add so much flour that dough does not stick to your hands; it should be slightly tacky. Knead dough for five minutes in mixer with dough hook, or knead with hands on a floured surface.
Place dough in buttered bowl and turn over to coat entire surface. Cover with plastic wrap and let rise in warm place about 1 hour or until doubled.
Punch down dough and turn out onto lightly floured surface. Knead a few times and cut into two pieces. Roll out each piece to 12x9-inch rectangles.
For the Filling:
Generously brush rolled dough pieces with melted butter. Sprinkle each with half of cinnamon sugar mixture and roll them up jelly-roll style. Cut rolls down center lengthwise and carefully braid the pieces together by crossing them over one another. Using spatula or bench scraper, carefully lift braided loaf into buttered 9-inch loaf pan; repeat with remaining loaf. Cover pans with plastic wrap and let rise until doubled, about 1 hour.
Preheat oven to 350°F. Bake loaves until golden brown, about 20-25 minutes, or until internal temperature is 190°F.
Serve slices of bread warm from pan, or let loaves cool for 10 minutes before turning them out onto wire rack to cool fully.