Make the dough: 
In a stand mixer fitted with the dough hook, combine the bread flour, softened butter, warm milk, honey, yeast, egg, and salt. Mix on low speed until just combined. Increase to medium speed and knead until the dough is smooth and slightly elastic, about 4–5 minutes.

First rise:
 Cover the bowl with plastic wrap or a kitchen towel and let the dough sit at room temperature until it doubles in size, about 2 hours.

Shape the rolls:
 Lightly flour your work surface. Turn the dough out and divide it into 8 equal pieces. To shape each piece into a smooth ball. Gently flatten the dough slightly. Fold the edges toward the center and pinch to seal. Place seam-side down on your work surface and lightly roll in a circular motion until smooth. Place the shaped rolls in a lightly greased cast iron pan, casserole dish, or baking pan.

Second rise: 
Cover the rolls and let them rise until puffy, about 45 minutes to 1 hour.

Preheat the oven:
 Preheat to 350°F (175°C).

Bake the rolls:
 Brush the tops with the whisked egg. Bake for 25–28 minutes, or until golden brown on top.

Finish:
 Remove from the oven and immediately brush with melted butter. Sprinkle with flaky sea salt.