In a large bowl, whisk together the all-purpose flour, granulated sugar, and salt. Set aside.
In a pot on the stove melt the butter with the milk. The mixture should be just warm to the touch so as not to kill the yeast. Remove from the stove and add the packet of instant yeast into the butter mixture and whisk until the yeast is dissolved. Add the egg and mix.
Pour the wet ingredients into the dry ingredients and mix together until a dough is formed. Pour out the mixture onto a floured countertop and knead for about 5 minutes or until a nice ball has formed.
Place the dough balll into a greased bowl and cover with a clean towel. Let rise in a warm environment for about 60-90 minutes or until the dough has doubled in size. While the dough is rising, prepare the cinnamon sugar filling and the cream cheese icing.
Cinnamon Sugar Filling: In a small bowl, mix together the brown sugar and cinnamon.
Cream Cheese Icing: In a medium bowl, beat the cream cheese on its own for about 2 minutes until it is whipped. Add the unsalted butter, icing sugar, and vanilla extract to the whipped cream cheese and beat again for about 2-3 minutes on medium speed until it is fully mixed together and a sweet icing has formed. Set aside.
Preheat the oven to 375℉/190℃/Gas Mark 5.
Once the dough has risen, pour it out onto a clean countertop and using a rolling pin, roll out the dough to approximately 8”x14” wide. Spread the butter onto the dough and sprinkle the cinnamon sugar filling all over the buttered dough until it is all used up. Roll the dough tightly into a long, log shaped roll.
Slice the cinnamon log into about 10-14 cinnamon rolls and place into a greased 9x9 dish. Bake for 28-30 minutes or until just brown and golden.
Remove from the oven and spread the cream cheese icing over all of the rolls and enjoy!