01 - In the bowl of a stand mixer, combine the bread flour, sugar, salt, and instant dry yeast. Whisk together until evenly distributed.
02 - Add the eggs and warm milk to the dry mixture. Mix on low speed using the dough hook attachment until a shaggy dough begins to come together.
03 - Gradually add the softened butter cubes, a few at a time, allowing each addition to fully incorporate before adding more. Continue kneading on medium speed for 10 to 15 minutes until the dough is smooth, elastic, and slightly tacky to the touch.
04 - Cover the bowl tightly with plastic wrap or a damp kitchen towel. Place in a warm, draft-free spot and let the dough rise until doubled in size, approximately 1½ to 2 hours.
05 - Gently punch down the risen dough and turn it out onto a lightly floured surface. Shape into your desired form — a classic loaf, braid, or individual rolls — and place into a greased 9×5-inch loaf pan or on a parchment-lined baking sheet.
06 - Cover the shaped dough loosely and let it proof again for 45 to 60 minutes until visibly puffy and nearly doubled.
07 - Preheat the oven to 350°F (180°C), positioning the rack in the center.
08 - Whisk together the egg and milk to create the egg wash. Using a pastry brush, gently brush the top of the loaf with an even, thin coating for a rich golden finish.
09 - Bake for 25 to 30 minutes until the top is deep golden brown and the loaf sounds hollow when tapped on the bottom. If browning too quickly, tent loosely with aluminum foil during the last 10 minutes.
10 - Allow the bread to cool in the pan for 10 minutes, then turn out onto a wire cooling rack. Let it cool completely before slicing to preserve the crumb structure.