In a small saucepan, gently heat the milk until warm (about 110°F). Pour the warm milk into a large mixing bowl. Add the instant yeast and 1 tablespoon of sugar; let it sit for 5-10 minutes until frothy.
Add the remaining sugar, eggs, oil, and vanilla extract to the yeast mixture. Stir well until combined.
Gradually add the flour and salt to the wet mixture. Mix until a soft dough forms. Knead the dough on a floured surface for about 5-7 minutes until smooth and elastic.
Place the dough in a greased bowl, cover with a damp cloth, and let it rise in a warm place for about 1 hour or until doubled in size.
In a small bowl, combine brown sugar and cinnamon. Set aside.
Punch down the risen dough and roll it out into a rectangle about ¼ inch thick. Spread the softened butter over the surface, then sprinkle evenly with the cinnamon-sugar mixture.
Starting from the long side, tightly roll up the dough into a log. Slice into 12 equal pieces and place them in a greased baking dish.
Cover the rolls with a cloth and let them rise for another 30 minutes.
Preheat your oven to 375°F (190°C). Bake the rolls for 20-25 minutes or until golden brown.
While the rolls bake, beat the cream cheese, powdered sugar, vanilla extract, and 2 tablespoons of milk until smooth. Add more milk if needed to reach your desired consistency.
Once baked, let the cinnamon rolls cool slightly. Drizzle with the cream cheese icing and enjoy!