01 - In the bowl of a stand mixer, whisk together the bread flour, granulated sugar, fine sea salt, and instant dry yeast until evenly distributed.
02 - Add the eggs and warmed milk to the dry mixture. Mix on low speed using the dough hook attachment until a shaggy dough begins to come together, about 2 minutes.
03 - Gradually add the softened butter cubes, a few pieces at a time, allowing each addition to fully blend 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 volume, approximately 1½ to 2 hours.
05 - Gently punch down the risen dough and turn it out onto a lightly floured surface. Shape into your preferred form — a classic loaf, a braid, or individual rolls — and place into a greased 9×5-inch loaf pan or onto a parchment-lined baking sheet.
06 - Cover the shaped dough loosely with a damp towel or oiled plastic wrap. Let it proof for 45 to 60 minutes until puffy and nearly doubled.
07 - While the dough undergoes its second rise, preheat the oven to 350°F (180°C), positioning the rack in the center.
08 - Whisk together 1 egg and 1 tablespoon of milk to create the egg wash. Using a pastry brush, lightly coat the top of the loaf for a deep golden, glossy crust.
09 - Bake on the center rack for 25 to 30 minutes, rotating halfway through, until the crust is a rich golden brown and the loaf sounds hollow when tapped on the bottom.
10 - Allow the bread to rest in the pan for 10 minutes, then turn it out onto a wire cooling rack. Let it cool completely before slicing for clean, even cuts.