Activate the yeast: Combine warm milk, yeast, and sugar in a large bowl. Let sit 5–10 minutes until foamy.
Make the dough: Add melted butter, egg, and salt. Mix in flour, one cup at a time, until a soft dough forms. Knead 5–7 minutes by hand (or 3–4 minutes in a mixer) until smooth and elastic.
First rise: Place the dough in a greased bowl, cover, and let rise for 1–1½ hours until doubled.
Roll + fill: Roll dough into a large rectangle about ¼-inch thick. Spread softened butter evenly, then sprinkle the cinnamon-brown sugar mixture generously over the top.
Roll + cut: Roll tightly from the long edge. Using dental floss or a sharp knife, cut into 10–12 rolls.
Second rise: Place rolls in a greased baking dish, cover, and let rise 30–45 minutes until puffy.
Bake: Bake at 350°F for 22–25 minutes until just golden.
Glaze: Whip cream cheese, butter, powdered sugar, vanilla, and milk until smooth. Spread generously over warm rolls.
Notes
Make-ahead: After cutting the rolls, cover tightly and refrigerate overnight. In the morning, let sit at room temperature for 30 minutes and bake.