In a large mixing bowl or using a stand mixer fitted with the dough hook, combine water, 2/3 cup (167 g) sugar, and yeast. When foamy, add salt, softened butter, milk, and 5 cups (675 g) flour. Stir until well mixed then add remaining 2 1/2 cups flour, 1/2 cup at a time. Tip dough out and onto a lightly floured surface, knead until a soft dough forms, adding more flour if needed, 3 to 5 minutes.
Place dough in a lightly-oiled bowl and turn to coat. Cover with a clean cloth and set in a warm, draft-free area until doubled in size, about 45 minutes.
Preheat oven to 350°F (180°C).
Punch down dough and roll out on a lightly floured surface into a 10- by 4-inch (25- by 10-cm) rectangle. Brush with half of the melted butter.
In a small bowl, combine remaining sugar, brown sugar, and cinnamon; sprinkle evenly over the top of the dough. Fold the dough into thirds and then roll out to a 12- by 4-inch (30- by 10-cm) rectangle.
Divide the dough lengthwise into 3 equal pieces and braid together. Bring ends together and pinch to form a circle.
Coat a 5 1/2 quart or larger Dutch oven with nonstick cooking spray. Place the braided bread in the Dutch oven, cover with the lid and bake until golden brown and the internal temperature reaches 190°F (88°C), 55 to 70 minutes. Remove bread from the oven, place on a wire rack and brush with the remaining melted butter. Let cool.