In a stand mixer bowl, add in 2 cups of flour and yeast. Stir to combine.
In a medium saucepan, add in the milk, butter, sugar, and salt. Place over medium heat until the butter is melted and the sugar is dissolved. Don't let it come up to a boil. Let it cool to 11o - 115 degrees.
Pour the milk mixture and eggs into the dry ingredients. Using the dough hook, place on 2 or the recommended setting for using the dough hook on your mixer.
Once combined, add in 1 additional cup of bread flour and use the dough hook to bring it together. As soon as the flour is worked in and the dough pulls away from the sides of the bowl, stop the mixer. If you're not paying attention, the dough will pass this stage and begin sticking to the sides again. If this happens, remove the dough from the bowl and hand knead in about 1/4 to 1/2 cup of flour that isn't included in the recipe ingredients.
Add the vegetable oil to the bowl with the dough and roll the dough around until it's coated. Cover loosely with a plastic wrap and/or tea towel. Let it rise until the dough is doubled, about 1 hour. I set the bowl on the stovetop with the oven set to 245 degrees.
Once the dough has doubled, turn it out onto a well-floured surface. Use the remaining 1/4 cup of flour to dust the surface.
Using your hands or a rolling pin, roll the dough out into a 20"x12" rectangle.
Add bits of butter all over the dough. Using your hands or an offset spatula, spread the butter evenly on the dough. Spread all the way to the edges.
In a small bowl, add in the brown sugar and cinnamon. Stir to combine.
Sprinkle the cinnamon and sugar on the butter. Using your hands, move the cinnamon and sugar to cover any bare spots and then push the cinnamon and sugar into the butter.
Starting on the 20-inch side, roll the dough into a log. Pinch the dough along the log so it holds together when it's sliced. Push in both ends of the log also.
Mark out where you'll want to cut the dough. I marked the log into 8 thick slices. Grab a long piece of floss and slide it underneath the log. Crisscross the floss and pull together to cut the rolls. You can also use a sharp knife, but I find that it pinches the dough.
Place the rolls into a greased 7x11 pan. Cover with the tea towel and let rise for 30 minutes.
Preheat oven to 350 degrees. Place the cinnamon rolls into the oven and bake for 30 - 40 minutes until the tops are golden brown and when you gently tug on the center rolls, it doesn't look doughy. While the cinnamon rolls are baking, make the frosting to put on the rolls while they're still hot.
In a large bowl, add in the cream cheese and butter. Beat on medium with the hand mixer until creamy.
Add in the powdered sugar and vanilla extract. Beat until the powdered sugar is incorporated and the icing is smooth.
Frost the tops of the hot cinnamon rolls. You can add as much or as little as you would like. If you let the cinnamon rolls cool, you can also microwave the icing for 30 seconds and pour it on to the cinnamon rolls.