01 - In the bowl of a stand mixer, whisk together the bread flour, sugar, salt, and instant dry yeast until evenly distributed.
02 - Add the eggs and warmed milk to the dry ingredients. 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 at a time, mixing on medium-low speed after each addition until fully absorbed. Continue kneading 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 to release excess air. Transfer to a lightly floured surface and shape into your desired form — a classic loaf, a braided crown, or individual rolls. Place the shaped dough into a greased 9×5-inch loaf pan or onto a parchment-lined baking sheet.
06 - Cover loosely and let the shaped dough rise again for 45 to 60 minutes until puffy and nearly doubled.
07 - While the dough completes its second rise, preheat the oven to 350°F (180°C). Position the rack in the center of the oven.
08 - Whisk together 1 egg and 1 tablespoon milk in a small bowl. Using a pastry brush, gently brush the egg wash over the top of the loaf for a rich golden-brown shine.
09 - Bake on the center rack for 25 to 30 minutes, until the crust is deep golden brown and the loaf sounds hollow when tapped on the bottom. If the top browns too quickly, tent loosely with aluminum foil during the last 10 minutes.
10 - Allow the loaf to cool in the pan for 10 minutes, then turn out onto a wire rack. Let cool completely before slicing for the cleanest cuts and best texture.