In the bowl of a stand mixer fitted with the dough hook, whisk together the bread flour, sugar, yeast, and salt.
Add the warm milk and eggs. Knead on low until the dough comes together, about 2 minutes.
Add the butter a half-tablespoon at a time, fully incorporating each before adding the next. Knead until elastic and tacky, about 10 minutes.
Transfer to a lightly oiled bowl, turn to coat, cover, and rise until doubled, 45 minutes to 1 hour.
Turn out onto a floured surface, press into a circle, and cut into 8 pieces (about 100g each).
Shape each into a smooth ball, place on a lined baking sheet a few inches apart, and flatten to about 3 inches wide.
Cover and rise again until doubled, 30–40 minutes.
Preheat oven to 400°F. Brush with egg wash.
Bake 12–15 minutes, rotating halfway, until golden brown.
Cool completely before slicing.