In the bowl of a stand mixer fitted with the hook attachment, add the warm milk, yeast, sugar, salt, softened butter, egg, and 3 cups flour. Mix on LOW speed fro 2 minutes, then increase speed to knead for 2-3 minutes.
Add 1/2 cup more flour at a time, kneading until well incorporated before adding the next batch of flour. Knead until a soft and pliable dough. You may not end up using all the flour.
Cover the bowl and place inside your oven with the light ON (but oven turned OFF) to rise for 30 minutes.
Divide the dough into 16 even pieces. Roll into tight balls on a clean surface.
Place in a greased 9x13" baking pan. Cover with plastic wrap and place in a warm environment to rise another 30 minutes to 1 hour, until doubled in size.
Preheat oven to 375F.
Brush with a beaten egg and the melted butter to bake 13-16 minutes, just until golden on top. Be careful not to overtake or they will dry out.
After you take them out of the oven, let cool for 10 minutes then drizzle honey over the dinner rolls. Garnish with flaky salt to enjoy!