In the bowl of a stand mixer, or a large mixing bowl, whisk together 3 ½ cups of flour, instant yeast, sugar, and salt.
Pour in the warm milk (should be heated to 120°F - 130°F), cooled melted butter, and egg. Add the dough hook if using a stand mixer. Mix on low speed, scraping the bowl to fully incorporate the flour, until a sticky, shaggy dough is formed. This may take about 5 -10 minutes.
Gradually add in ½ cup of flour at a time, mixing and checking the dough before adding in another ½ cup of flour. You may not need all 5 cups of flour. You will want to mix the dough until it starts pulling away from the sides of the bowl and is smooth and slightly tacky. This should take about 2-3 minutes with a stand mixer or 3-5 minutes by hand.
Knead the dough at medium speed with the dough hook attachment for 5-6 minutes or by hand for 8-10 minutes.
Lightly grease a large bowl. Add in the dough and turn it once to coat with the oil from the bowl. Cover with plastic wrap or a clean, lint free kitchen towel. Put in a warm area for 30-40 minutes, to allow the dough to double in size and when pressing a finger about ½” into the dough the bounce back should be slow.
Remove the towel or plastic and punch down the dough to deflate it. Turn it out onto a floured surface.
Divide the dough into 15 equal pieces, about 2 ounces each. Shape each piece of dough into a smooth ball, tucking the edges under and rolling it. Place each roll into a lightly greased 9x13-inch baking pan keeping a little space between each. 1 15
Cover the rolls again with a towel or plastic wrap, let rise again for another 30-40 minutes. This may take longer depending on the warmth of your environment,, you want them pretty poofy.
About 20 minutes before rolls are due to be ready, preheat the oven to 375° F.
Place the rolls on the middle rack of the oven and bake for 13-18 minutes until lightly browned. Brush baked rolls with melted butter.