In a small saucepan over medium-low heat, warm the milk just until small bubbles appear around the edges.
Add the sugar, butter, and salt to a stand mixer bowl, then pour in the warm milk and stir until the butter is melted.
Sprinkle on the yeast, stir, and let it stand to dissolve and become foamy (about 10 minutes).
Add the egg and 2 cups of flour.
Use the dough hook to begin mixing the dough, gradually adding the remaining flour until incorporated.
Turn the dough out onto a lightly floured surface and knead for 5 minutes until smooth and elastic.
Place the dough in a large, oiled bowl and cover.
Allow the dough to rise until doubled (about 1.5 hours).
Line 2 baking sheets with parchment paper.
Punch the dough down and divide it in half.
Shape the dough into 2 balls. Return one ball to the oiled bowl and cover.
Roll the other ball into a circle about 12 inches in diameter.
Brush on a thin layer of melted butter.
Cut the circle into quarters, then cut each quarter into 3 wedges.
Beginning at the wide end, roll up each wedge, then curve the ends toward one another to form a crescent.
Evenly space the crescents with the points tucked underneath on one of the prepared baking sheets, then cover with a damp kitchen towel.
Repeat the process with the remaining dough, then brush all of the rolls with some of the remaining melted butter.
Preheat the oven to 400 F while the rolls proof for 20 minutes.
Bake the crescent rolls one pan at a time for 10-12 minutes or until golden brown, then move them to a cooling rack and brush them with the remaining melted butter while still hot.