Step 1: Prepare the Starter
In a small saucepan, whisk together the bread flour, milk, and water until smooth. Over medium-low heat, cook the mixture, stirring constantly, until it thickens to a pourable consistency—this should take around 10 minutes. When done, the mixture should leave visible tracks when stirred. Remove from heat, transfer to a measuring cup, and cover the surface with plastic wrap. Allow it to cool to room temperature.
Step 2: Combine Dry Ingredients
In the bowl of a stand mixer, combine bread flour, sugar, yeast, and salt. Mix briefly to ensure even distribution of the ingredients.
Step 3: Add Wet Ingredients
Add the egg, warm milk, and half of the cooled starter to the dry ingredients. Turn the mixer on low speed and mix for about 5 minutes, allowing the dough to form.
Step 4: Incorporate Butter
Add the softened butter in small pieces. Continue mixing for an additional 10 to 12 minutes until the dough becomes smooth, springy, and slightly tacky, but not sticky.
Step 5: First Rise
Lightly butter a bowl and shape the dough into a ball. Place it in the bowl, cover with a kitchen towel, and let it rise in a warm spot for 40 to 60 minutes, or until it has doubled in size.
Step 6: Shape the Dough
Once the dough has risen, punch it down and transfer it to a flat surface. Divide the dough in half and shape each portion into a ball. Allow them to rest, covered, for 15 minutes.
Step 7: Prepare the Pan
While the dough is resting, preheat your oven to 350°F (175°C). Butter a 9-by-5-inch loaf pan generously.
Step 8: Roll the Dough
Using a rolling pin, gently flatten one dough ball into an oval shape about 12 inches long and 6 inches wide.
Step 9: Shape into a Log
Fold the top and bottom edges of the oval towards the center to form a rough square. Then, starting from one edge, roll the dough into a log, sealing the edge as you go. Place the log seam side down in the prepared loaf pan. Repeat the same process with the second dough ball, positioning it next to the first in the pan.
Step 10: Second Rise
Cover the loaf pan and allow the dough to rest for 30 to 40 minutes. The dough should rise until it peaks over the edge of the pan, with both logs meeting in the middle.
Step 11: Bake the Bread
Brush the tops of the dough logs with a little warm milk. Bake in the preheated oven for 35 to 40 minutes, or until the bread is golden brown and puffed.
Step 12: Cool the Bread
Allow the bread to cool in the pan for 10 minutes before transferring it to a wire rack. Let it cool completely for at least an hour to prevent the crumb from deflating.