Start by combining the warm milk, sugar, and yeast into a medium bowl. With a spoon, stir gently to combine and set aside for 5 minutes
After 5 minutes, add the flour, salt, butter, egg and milk mixture into the base of a stand mixer with the whisk attachment. Beat on low until combined
After it is combined, mix on medium for 2 minutes. After 2 minutes, the dough should begin to pull away from the edges. At this stage, if the mixture seems like it would be impossible to knead by hand, add another tablespoon or two of flour until it is a kneadable consistency. Knead for 3 more minutes in the mixer (this can also be done by hand but is much easier in a mixer since it is a sticky dough)
Once the dough is kneaded, grease a bowl with butter and add the dough. Cover with a towel and let rise for 90 minutes - 2 hours (until it has doubled in size)
Grease a 9x13” glass baking dish. Set aside
Punch down the dough and cut it into around 12 pieces (~2 oz each in weight). Using your hands, gently form each piece into a round ball. Place each rounded piece into the baking dish leaving even separation between each piece. Cover with a towel and let rise for 90 minutes or until doubled in size
Pre-heat the oven to 375 degrees F
Brush the top of the rolls with egg wash and bake for 15-18 minutes until golden brown on top
Remove the rolls from the oven and brush with melted butter and sprinkle with flaky salt
Serve warm