Preheat the oven to 170 degrees F. This is for the first dough rise cycle.
In a bowl, dissolve the yeast in warm milk. I microwaved the milk for 10 seconds. It should be just barely warm to the touch but not hot. If it is hot it will kill the yeast and if it's too cold it won't activate it.
In a separate bowl, add sugar, melted butter, salt, egg, and flour. Mix well.
Pour the yeast milk mixture into the flour mixture. Mix until well combined. If using a stand mixer use the dough hook.
Scrape down the sides of the bowl to form a dough ball, it will be very sticky. Pour some oil over the dough in the bowl and turn to coat.
Cover the bowl with a warm damp towel tea towel.
Turn the oven OFF, place the covered dough bowl inside and let rise 45 min to 1 hour or until the dough has doubled in size.
Take the dough out of the oven and re-heat the oven to 170 degrees F. This is for the second rise cycle.
Place the dough on a floured surface and coat both sides with flour. Roll or shape the dough until it is approximately 4 inches wide by 9 inches long.
Use a knife or pizza cutter to cut the dough in half lengthwise to make two strips each 2 x 9 inches.
For the Filling:
Melt the 2 tablespoons of butter and brush it onto the dough strips.
Combine the brown sugar and cinnamon in a bowl. Sprinkle the mixture evenly over the dough strips.
Carefully, starting from the short edge, roll each of the dough strips down to the opposite edges.
Spray two 7 ounce oven safe ramekin dishes with non-stick cooking spray.
Place the rolls into the ramekins and gently spray them with more non-stick cooking spray.
Turn the oven OFF, place the ramekins inside and let them rise again for another 20 - 30 minutes until they double in size. Check them often so they don't spill over, they will rise more during the baking cycle.
Remove the ramekins from the oven and preheat it to 350 degrees F.
Bake the cinnamon rolls for 15 - 20 minutes or until golden brown.
For the Icing:
While the rolls are baking, melt the 1 tablespoon of butter.
In a bowl, mix the butter, powdered sugar, cream cheese, and vanilla. Beat with a mixer or stand mixer until well combined and fluffy.
After the cinnamon rolls have cooled about 5 - 10 minutes, spread each generously with icing.