In a large mixing bowl or the bowl of a stand mixer, combine the flour, yeast, sugar, and salt.
Add the egg and warmed milk. Mix until a shaggy dough forms.
Knead the dough by hand or with a stand mixer on medium speed for 8-10 minutes, until smooth and elastic. Add the softened butter in small pieces and continue kneading until fully incorporated.
Shape the dough into a ball and place it in a lightly greased bowl. Cover with a clean kitchen towel or plastic wrap. Let the dough rise in a warm place for about 1-1½ hours, or until it doubles in size.
Punch down the risen dough to release air. Turn it out onto a lightly floured surface. Roll the dough into a rectangle, then roll it tightly into a log to fit the loaf pan.
Place the shaped dough into a greased 9x5-inch loaf pan. Cover the pan and let the dough rise again in a warm place for 45-60 minutes, or until it reaches just above the edge of the pan.
Preheat your oven to 350°F (175°C). Brush the top of the loaf with the egg wash (whisk together the egg and milk).
Bake for 25-30 minutes, or until the top is golden brown and the loaf sounds hollow when tapped.
Remove the bread from the oven and allow it to cool in the pan for 10 minutes. Then, transfer to a wire rack to cool completely before slicing.