Dough: In a large bowl, whisk together yeast, warm milk, and granulated sugar. Let stand for 5-10 minutes until foamy.
Whisk in melted butter and egg. Gradually add salt and 3 cups of flour, mixing until combined.
Add the remaining 1 cup of flour, a little at a time, until a soft dough forms. Turn out onto a lightly floured surface and knead for 6-8 minutes until smooth and elastic.
Place dough in a greased bowl, cover, and let rise in a warm place for 1-2 hours, or until doubled in size.
Filling: In a medium bowl, combine softened butter, brown sugar, and cinnamon. Mix until smooth and spreadable.
Assemble: Punch down the risen dough. On a lightly floured surface, roll the dough into a 12×18 inch rectangle.
Spread the cinnamon-sugar filling evenly over the dough, leaving a ½ inch border on one long edge.
Starting from the long edge with the filling, tightly roll up the dough.
Cut the roll into 12 equal slices.
Place slices, cut-side up, in a greased 9×13 inch baking pan.
Second Rise: Cover the pan loosely and let the rolls rise for another 30-60 minutes, or until puffy.
Baking: Preheat oven to 375°F (190°C).
Bake for 20-25 minutes, or until golden brown and cooked through.
Frosting: While rolls are baking or cooling, beat together softened cream cheese and softened butter until smooth.
Add powdered sugar and vanilla extract, beating until creamy. Add milk if needed to reach desired consistency.
Remove rolls from oven and let cool slightly. Spread frosting generously over warm rolls.