In a mixing bowl, combine warm milk, active dry yeast, and granulated sugar. Let stand 5–10 minutes until foamy.
Whisk in the egg, egg yolk, and melted butter.
Add the flour and salt. Mix until a soft dough forms, then knead 8–10 minutes until smooth and elastic (by hand or mixer).
Place dough in a greased bowl, cover, and let rise in a warm place for 1 to 1 1/2 hours, until doubled.
In a small bowl, make the filling by mixing softened butter, brown sugar, and ground cinnamon until spreadable.
Punch down dough and roll into a 12×18-inch rectangle on a lightly floured surface.
Spread the cinnamon filling evenly over the dough, leaving a small 1/2-inch border on one long side.
Roll up tightly from the opposite long side into a log. Seal the edge. Slice into 12 even rolls using unflavored dental floss or a sharp knife.
Arrange rolls in a greased 9×13-inch baking dish. Cover and let rise 30–45 minutes until puffy.
Preheat oven to 350°F (175°C). Bake 20–25 minutes, until golden and set in the center.
For the glaze, beat cream cheese and softened butter until smooth. Add powdered sugar and vanilla; beat again. Thin with milk, a little at a time, to desired consistency.
Spread glaze over warm rolls and serve.