To Make the Dough:

1. In the bowl of an electric stand mixer, sprinkle yeast over warm milk, and whisk to combine. Let the mixture stand for about 10 minutes, until foamy.
2. Remove the whisk attachment and replace with the paddle attachment. Add flour, butter, sugar, eggs, and salt. Mix on low speed until everything’s combined, about 3 minutes.
3. Raise speed to medium-low, and continue to mix until the dough is smooth and pulls away from the sides of the bowl, about 3-6 minutes more. Turn out the dough onto a lightly floured surface, and pat it into a big round.
4. Sprinkle with 1 tablespoon cinnamon, and knead and fold until it’s incorporated, about 5 minutes. You can also knead this with the dough hook in the bowl of your mixer for 3 minutes on medium-low speed.
5. Lightly oil a large mixing bowl and a large piece of plastic wrap. Place the dough in the bowl and cover with the oiled plastic wrap with the oil side down. Let rise in a warm place until doubled in size, about 1 hour.
6. Return the dough to a lightly floured work surface, and pat it into a rectangle. In the same way that you would fold a letter, fold the bottom third of the dough up, and the top third down, so they are overlapping. Fold the right and left sides over so they overlap, then gently press down to seal.
7. Return the dough into the bowl with the sealed side down. Let it rise again until doubled in size, about 40 minutes.
8. Generously butter two 9-by-5-inch loaf pans, and set them aside. Lightly oil two pieces of plastic wrap that will be used to cover the pans.

To Make the Filling, Shape, and Bake:

1. Stir together sugar and cinnamon with 2 tablespoons water and cooled melted butter in a small bowl until combined.
2. Return the dough to a lightly floured work surface, and divide into two equal portions. Roll each into a rectangle that’s 2 inches wider on each side short side and 1 inch longer on each long side than the base of the pans, i.e. 9 inches by 11 inches.
3. Lightly beat the remaining egg. Brush the dough with half of the beaten egg, and save the rest. Sprinkle each with half of the filling. Do not leave an uncoated border around the edges.
4. With the short end of the rectangle facing you, fold in both of the long sides of the dough to the center, so that they meet but do not overlap.
5. Roll the dough towards you, gently pressing to form a tight log. Roll back and forth to seal the seam.
6. Place loaves in prepared pans, seam side down. Cover loosely with oiled plastic wrap, and let rest in a warm place, about 30 minutes or until doubled in size.
7. Meanwhile, preheat oven to 425°F.
8. Brush the tops of the loaves with the remaining beaten egg, and transfer pans to the oven. Bake, rotating pans halfway through, until loaves are golden brown, about 45 minutes. Keep an eye on them! If the tops begin to brown too quickly, tent with aluminum foil RIGHT AWAY.
9. Remove from the oven. Turn out the bread onto a wire rack to cool completely before slicing. The bread can be kept, wrapped tightly in plastic at room temperature, for up to 4 days.