Heat the milk in a saucepan (or in the microwave) until it is just warm, 100-110F.
Mix together the flour, sugar, yeast, and salt in a large bowl.
Make a well in the center of the flour. Pour in the warm milk, melted butter, and egg. Stir vigorously with a large spoon until combined. The dough will be thick and sticky.
Cover the bowl with either a damp cloth or plastic wrap and put it in a warm, draft free place to rise. Let rise for 1 1/2 - 2 hours. The dough will more than double in size.
Prep a 9x13 baking pan by spraying it with vegetable oil and cutting a piece of parchment to line the bottom and overhang the sides.
When your dough is ready, punch it down and then turn it out onto a well floured board.
Work it a little bit to deflate the bubbles, then divide the dough into 12 equal pieces. Dust with flour as needed to keep the dough from sticking.
Gather up each piece of dough, pulling the dough up and pinching it to make a ball. (The process photos in the post show how that's done.)
Once you've pinched up the dough into a ball, put it pinch side down onto the floured board and gently roll it around a little keeping the same side down. Then place the roll into the prepared baking pan. Continue until you have made 12 rolls.
Cover the rolls with a damp cloth or plastic wrap set it into a quiet spot in the kitchen to rise for 30-40 minutes. Or until just about doubled and the rolls fill the pan.
After the rolls have risen for 20 minutes, preheat the oven to 375F.
Bake the rolls for 17-20 minutes, or until they are golden brown.
While they are still hot, brush the rolls with melted butter.
Use the parchment paper to lift the rolls onto a cooling rack and let cool until warm or room temperature.