Warm milk until it's a little bit hot to the touch, sprinkle the yeast on top and let it activate until it foams up, about 10 to 15 minutes. Add in sugar, egg, egg yolk and melted butter and mix until well combined.
Stir in flour and salt and knead the dough on a floured surface for 8-10 minutes. If you have a stand mixer you can knead the dough on medium speed for 8 minutes. It should form a slightly sticky ball. If it sticks to the bowl you can add a tablespoon or two of flour.
When the dough ball has formed, transfer it in a greased bowl, cover with plastic wrap and allow it to rise for 1 hour to 1 and a half hours, or until doubled in size.
After the first rise is complete, on a well floured surface use a rolling pin to form a 35/20 cm rectangle.
Spread softened butter on the dough, leaving a centimeter margin on the long side. Mix brown sugar with cinnamon and sprinkle over the dough, rubbing gently into the butter.
Roll the dough tightly, starting from the long side which has a margin and place it seam side down, making sure that the roll is sealed. Cut the ends of the roll, about 2 cm from each side, because they will not have enough cinnamon and sugar filling.
Divide and cut the dough with a serrated knife into 8 large pieces or 12 smaller ones.
Arrange them cut side up in a baking pan lined with parchment paper, cover with plastic wrap and let them rise again for 30-45 minutes, or until doubled in size.
After the second rise, bake them in a preheated oven at 180°C for 20-25 minutes, or until golden-brown.
While the rolls are baking, beat cream cheese, powdered sugar, butter and vanilla essence until smooth and creamy.
Let cinnamon rolls to cool down for 10 minutes, frost them with cream cheese and serve immediately. To reheat, place them in the microwave for 30-45 seconds.