In the bowl of stand mixer, stir together the milk and yeast. Add 1½ cups of flour followed by the butter, sugar, egg, and salt.

Beat with the paddle attachment at medium-low speed until combined. Scrape down the bowl and switch to the dough hook. Add another 1½ cups of flour and mix on medium until the dough forms a ball about, 2 to 3 minutes. Add the additional ¼ cup of flour a tablespoon at a time if needed.

Continue mixing for 2 minutes to knead the dough then finish off by hand until smooth and bounces back when pressed.

Place the dough in an oiled bowl, cover with plastic wrap, and place in a warm place to rise until doubled in size, 1 to 2 hours.

Once risen, grease a 9x13-inch baking dish with softened butter.

Puch down the dough and turn out onto a lightly floured surface. Divide into 15 equal pieces. Pinch the corners of each pieces together at the center, then flip over. Cup the ball with your hands and move in a tight circular motion to shape each ball. This will pull the edge in, creating a tight ball and smooth roll.

Place arrange the dough balls in the prepared pan evenly spaced apart, cover loosely with plastic wrap and allow to rise until visibly puffed or almost doubled in size, about 1 hour.

When the rolls look almost done rising, preheat the oven to 350°F.

Bake for 20 minutes or until very puffed and the tops are a deep golden brown. Brush the hot rolls with melted butter. You can serve them immediately or let them cool before serving.