In the bowl of a stand mixer combine the warm water, sugar, oil, salt, and eggs. Whisk to combine and break up eggs.
Add the all-purpose flour and yeast. Mix with the dough hook attachment until combined, 1 minute. Add 2 cups of the cake flour and continue mixing. As the dough mixes, add the remaining 1 cup of cake flour as needed, one tablespoon at a time, until the dough cleans the side of the mixing bowl and is smooth and elastic, 5-8 minutes.
With the mixer running on medium-low speed, add the butter one tablespoon at a time until it is all incorporated.
Remove the dough from the bowl and place in a greased clean bowl. Cover tightly and let rise in a warm place until doubled in size, 45-60 minutes.
For the filling: Melt butter and set aside. In a small bowl combine the sugars and cinnamon. Whisk to break up brown sugar and ensure there are no lumps. Set aside.
For the caramel roll variation: Prepare caramel sauce while the rolls are rising. In a small saucepan, combine the butter, water, dark brown sugar, corn syrup, and salt. Heat until the mixture begins to boil. Simmer for 2 minutes then remove from heat and cool. Pour directly into four greased 8-inch cake pans. Sprinkle with toasted chopped pecans and set aside.
Once the dough has doubled in size, punch down and divide into two equal pieces. On a well-floured surface, working with one piece at a time, roll out into a 16 x 18-inch rectangle.
Brush 3 tablespoons melted butter over the dough. Sprinkle with half of the prepared filling mixture.
Tightly roll up the dough starting with a long side. Squeeze the seams together to seal. Cut the roll into 16 individual rolls. Place in a) pans with prepared caramel, b) greased pans with no caramel, or c) on parchment-lined baking sheets 3 inches apart for individual rolls. Cover loosely with plastic wrap and allow to rise until doubled in size, 45-60 minutes. Repeat with second portion of dough.
While the dough is rising, preheat oven to 350°F.
Once risen, bake the rolls in a preheated oven until golden brown, 14-18 minutes. Remove from oven. If making frosted rolls, cool 10 minutes, remove from pans and frost (instructions follow). If making caramel variation, cool in the pan. After 1 hour, run a knife around the sides and invert onto a plate.
For the frosting: In the large bowl of a stand mixer (or hand mixer), combine the cream cheese and butter. Mix on medium speed until incorporated. Turn to medium-high until smooth, airy, and no lumps remain, approximately 3 minutes. Add the powdered sugar, vanilla, and 1 tablespoon milk. Mix on low until the sugar has incorporated. Add remaining milk or more sugar to create a spreadable frosting.
Calories for the sticky caramel roll variation: 380 calories