In a small bowl, combine the warm milk and yeast. Let it sit for about 5 minutes until it becomes frothy.
In a large mixing bowl, whisk together the melted butter, granulated sugar, and eggs. Add the frothy yeast mixture and mix well.
Gradually add the flour and salt to the wet ingredients, mixing until a dough forms. Knead the dough on a floured surface for about 5-7 minutes until smooth and elastic.
Place the dough in a greased bowl, cover it with a clean cloth, and let it rise in a warm place for about 1 hour or until it doubles in size.
Once risen, punch down the dough and roll it out on a floured surface into a large rectangle (about 16x24 inches).
Spread the softened butter over the dough, then sprinkle the brown sugar, cinnamon, and vanilla extract evenly on top.
Starting from one long side, roll the dough tightly into a log. Cut the log into 12 equal pieces and place them in a greased baking dish.
Cover the rolls with a cloth and let them rise for another 30 minutes. Preheat the oven to 350°F.
Bake the rolls for 20-25 minutes or until golden brown.
While the rolls are baking, prepare the icing by mixing the powdered sugar, cream cheese, and milk until smooth.
Once the rolls are out of the oven, let them cool for a few minutes before drizzling the icing over the top.