Combine warm milk and yeast in a large bowl; stand 5 minutes until foamy. Whisk in melted butter, eggs, sugar, and salt.
Gradually mix in flour into soft dough; knead on a floured surface 5-7 minutes until smooth and elastic. Place in a greased bowl; cover and rise in a warm spot 1 hour until doubled.
Punch down; roll into an 18x12-inch rectangle on a floured surface. Spread softened butter evenly; sprinkle with mixed brown sugar and cinnamon.
Roll tightly from long side; cut into 12 equal pieces in a greased 9x13-inch dish. Cover; rise 30 minutes.
Preheat oven to 350°F; bake 22-25 minutes until golden brown and puffed.
Meanwhile, beat cream cheese and butter until fluffy; beat in powdered sugar, vanilla, and milk until smooth and spreadable.
Cool rolls 5 minutes; frost generously while warm and serve immediately.