In a mixing bowl, combine warm milk, melted butter, and sugar. Stir in the yeast and let it sit for about 5 minutes, until foamy.
Add eggs, vanilla extract, and salt to the yeast mixture, and mix until well combined.
Gradually add the flour, one cup at a time, mixing with a wooden spoon until a soft dough forms. Once dough begins to pull away from the sides of the bowl, transfer it onto a floured surface.
Knead the dough for about 5-7 minutes, until it is smooth and elastic. Place the dough in a greased bowl, cover with plastic wrap, and let it rise in a warm place for about 1 hour, or until doubled in size.
Once the dough has risen, punch it down and roll it out into a rectangle (approximately 18x12 inches) on a floured surface.
In a small bowl, combine brown sugar and cinnamon. Spread the softened butter over the dough, followed by the cinnamon sugar mixture, ensuring it covers the entire surface.
Starting from the long edge, tightly roll the dough into a log. Cut the log into 12 equal pieces and place them in a greased baking dish, cut side up. Cover and let them rise for another 30 minutes.
Preheat the oven to 350°F (175°C). Bake the rolls for about 25 minutes, or until they are golden brown.
While the rolls are baking, prepare the cream cheese glaze by mixing softened cream cheese, powdered sugar, milk, and vanilla extract until smooth.
Drizzle the cream cheese glaze over the warm cinnamon rolls once they are out of the oven.