Melt butter in microwave. Warm milk in microwave-about 1 minute on medium.
Whisk melted butter, egg, milk and sweetened condensed milk together until well mixed.
Combine flour, sugar and salt in a bowl and mix well.
Add ingredients to your bread machine in order suggested by manufacturer. Mine is liquids, dry ingredients and yeast on top.
Set bread machine to dough cycle.
Prepare a baking pan about 8 X 8" or 9 X 9" with parchment paper on the bottom and slightly up the sides. Alternatively oil baking dish slightly.
Lightly oil your work surface and your hands. When the dough cycle is finished remove dough to work surface and punch it down. Fold it over on itself and form a fat log.
Divide dough into 3 equal portions and then divided each third into 3 more equal portions.
Shape the dough by stretching the top surface into a round smooth top. Twist and tuck the ends into the bottom of the dough ball. Transfer the dough to the baking pan spaced evenly apart in 3 X 3 rows. Cover the baking pan with plastic wrap and allow dough to rise for about 35 minutes.
Preheat oven to 350°.
Brush the tops of the rolls with milk. Place a sheet of parchment paper lightly over the top of the buns.
Bake the rolls for about 20 minute. Remove parchment paper and bake rolls 5 minutes more. You can test for doneness with an instant read thermometer. Middle roll should read 190°.
Remove from oven and allow rolls to cool for 5-10 minutes. Remove rolls from the pan and allow to cool further. When warm or room temperature pull or cut rolls apart.
Serve warm or at room temperature.
Rolls are best the day they are made but will keep another day in an airtight container at room temperature. If you want to keep them longer than the 2nd day freeze in an airtight bag.
Allow frozen rolls to thaw at room temperature and warm slightly in microwave if desired just before serving.