Warm milk in the microwave for 40-45 seconds. Transfer warm milk to the bowl of an electric mixer and sprinkle yeast on top. Add in sugar, egg, egg yolk and melted butter. Mix until well combined
Stir in flour and salt with a wooden spoon until a dough begins to form
Place dough hook on stand mixer and knead dough on medium speed for 8 minutes. Dough should form into a nice ball and be slightly sticky. If it's TOO sticky (meaning it's sticking to the bottom of the mixer), add in 2 tablespoons more bread flour
Transfer dough ball to a well-oiled bowl, cover with plastic wrap and a warm towel. Allow dough to rise for 1 hour to 1 ½ hours, or until doubled in size
After dough has doubled in size, transfer dough to a well-floured surface and roll out into a 14x9 inch rectangle. Spread softened butter over dough, leaving a ¼ inch margin at the far side of the dough
In a small bowl, mix together brown sugar and cinnamon. Use your hands to sprinkle mixture over the buttered dough, then rub the brown sugar mixture into the butter
Tightly roll dough up, starting from the 9-inch side and place seam side down making sure to seal the edges of the dough as best you can
Cut into 1 inch sections with a serrated knife to get 9 large pieces
Place cinnamon rolls in a greased 9x9 inch baking pan or round 9 inch cake pan. Line the pan with parchment paper. Cover with plastic wrap and a warm towel and let rise again for 30-45 minutes
Preheat oven to 350 degrees F. Remove plastic wrap and towel and bake cinnamon rolls for 20-25 minutes or until just slightly golden brown on the edges. You want to underbake them a little so they stay soft in the middle, that’s why we want them just slightly golden brown. Allow them to cool for 5-10 minutes before frosting
To make the frosting: In the bowl of an electric mixer, combine cream cheese, butter, powdered sugar and vanilla extract. Beat until smooth and fluffy. Spread over cinnamon rolls and serve immediately