Warm milk to 110°F. Melt butter and let cool briefly. In a bowl, whisk milk, butter, egg, sugar, and vanilla. Sprinkle yeast over top and let sit 2–3 minutes. Add flour and salt. Mix with dough hook 5–8 minutes until smooth ball forms.
Cover tightly with plastic wrap and a towel. Let rise 1 hour or until doubled.
Butter a 9×13 dish. In a bowl, mix brown sugar and cinnamon. Keep butter softened and ready.
Lightly flour surface. Roll dough into a 12×18 inch rectangle. Spread butter all over. Sprinkle cinnamon sugar. Roll tightly from the long 18-inch side for 9 rolls, or shorter side for 6 large. Slice evenly and place in dish.
Cover again. Let rise 30–45 minutes until puffy.
Preheat oven to 350°F. For extra gooey rolls, pour heavy cream between rolls before baking. Bake 28–32 minutes until golden.
Cool 10 minutes. Beat butter, cream cheese, vanilla, powdered sugar, and milk. Frost while rolls are still warm.
