01 - In a large bowl, combine flour, sugar, salt, and yeast, ensuring yeast does not directly contact salt. Pour in lukewarm milk, melted butter, and cracked egg. Mix thoroughly until a sticky, cohesive dough forms.
02 - Knead the dough on a lightly floured surface for 7 to 10 minutes until smooth and elastic. Transfer to a greased bowl, cover, and let rise in a warm area for 1 hour or until doubled in volume.
03 - Punch down the risen dough to release air. Shape into a rough rectangle, cover, and refrigerate for 30 minutes to firm.
04 - On a lightly floured surface, roll dough into a 12 x 16-inch rectangle. Arrange cold butter slices over two-thirds of the dough surface, leaving a 1-inch border.
05 - Fold the unbuttered third over the center buttered portion, then fold the remaining third over to create a neat rectangular packet. Rotate 90 degrees so the open edges face you.
06 - Roll the folded dough into a 12 x 16-inch rectangle again. Perform a letter fold by folding into thirds. Wrap tightly and refrigerate for 30 minutes.
07 - Repeat the rolling, folding, and chilling process two additional times for a total of three complete turns, chilling 30 minutes between each turn.
08 - After the final chill, roll dough to approximately 8 x 16 inches. Starting from a short edge, roll tightly into a cylindrical loaf shape, pinching the seam to seal.
09 - Place loaf seam-side down in a greased 9 x 5-inch loaf pan. Cover loosely with plastic wrap and let rise until doubled, about 1 hour.
10 - Preheat oven to 375°F. Whisk egg with 1 tablespoon milk until smooth. Brush the entire surface of the risen loaf with egg wash.
11 - Bake for 35 to 40 minutes until deep golden brown and the loaf sounds hollow when tapped on the bottom. Tent loosely with foil if the top browns too quickly.
12 - Allow the loaf to cool in the pan for 10 minutes, then transfer to a wire rack. Cool completely before slicing for clean, even cuts.