In a large bowl, dissolve yeast in warm water. Add the milk, butter, sugar, egg, salt and 2 cups flour; beat until smooth. Add enough remaining flour to form a soft dough.
Turn onto a floured surface; knead until smooth and elastic, about 6-8 minutes. Place in a greased bowl, turning once to grease top. Cover and let rise in a warm place until doubled, about 1 hour.
Punch dough down. Turn onto a lightly floured surface; divide in half. Roll each portion into a 12-in. circle; cut each circle into 12 wedges. Roll up wedges from the wide end and place point side down 2 in. apart on greased baking sheets. Curve ends to form a crescent.
Cover and let rise in a warm place until doubled, about 30 minutes. Bake at 350° for 12-15 minutes or until golden brown. Remove from pans to wire racks.
For glaze, heat butter in a small saucepan until golden brown; remove from the heat. In a bowl, whisk the confectioners' sugar, cinnamon, vanilla and browned butter until smooth. Whisk in enough hot water to achieve spreading consistency. Brush over warm rolls.