Combine warm milk (110°F / 43°C), sugar, and yeast in your stand mixer bowl and let sit for 5 minutes until foamy and bubbly.
Add melted butter, egg, and vanilla extract to the yeast mixture and mix on low speed until well combined.
Gradually add flour and salt one cup at a time, then knead with the dough hook on medium speed for 5–6 minutes until the dough is smooth, elastic, and slightly tacky.
Transfer dough to a greased bowl, cover with a kitchen towel, and let rise in a warm, draft-free spot for 45–60 minutes until doubled in size.
While the dough rises, mix softened butter, brown sugar, and cinnamon together until a smooth, spreadable paste forms; set aside at room temperature.
Punch down the risen dough, transfer to a floured surface, and roll into a 16x12 inch rectangle about 1/4 inch thick.
Spread the cinnamon filling evenly over the dough, leaving a 1/2 inch border along one long edge.
Tightly roll the dough from the filled long edge, pinch the seam shut, then cut into 12 equal slices using a sharp knife or unflavored dental floss.
Arrange rolls in a generously greased 9x13 inch baking dish, cover, and let rise in a warm place for 30–45 minutes until puffed and touching.
Preheat oven to 350°F (175°C) and bake rolls for 25–30 minutes until golden brown on top and the internal temperature reaches 190°F (88°C).
Beat cream cheese and butter until fluffy, gradually add powdered sugar, then mix in vanilla and enough milk to reach a smooth, spreadable consistency.
Cool rolls for 10 minutes, then generously spread cream cheese frosting over the top and serve warm.