Starting with the dough: using a stand mixer, with whisk attached, mix the egg yolks, whole egg, and sugar. Whisk until pale yellow. In a clean mixing bowl, add flour and salt, dry whisk, and set aside. Place buttermilk and butter into a heatproof container. Microwave for 90 seconds (make sure not to boil), remove, and stir the butter into the buttermilk. If steaming, set aside until the steam subsides. Turn the mixer to medium speed and slowly add the hot liquid mixture. Once poured, turn the mixer off and scrape down sides of bowl. Add the yeast and whisk for one more minute. Turn the mixture to low speed and add half of the flour. Mix to combine into a wet paste. Turn off mixture and detach the whisk attachment, replacing with dough hook. Add remaining flour and mix on medium until dough is combined into sticky ball, about two to three minutes. Take dough out of mixer and transfer to a lightly floured surface. Knead with your hands for about one minute. Dough should feel soft and pliable. Pour one tbsp of neutral oil into a clean mixing bowl, large enough for dough to double in size, and wipe all sides with oil. Place dough in oiled bowl and very lightly oil the top of the dough. Cover the top tightly with plastic wrap and cover the wrap with a clean towel. Set in a dry/warm area and allow to rise for two and a half hours. Dough should be doubled in size.
Turn dough over onto a lightly floured surface. Roll into a 12x18 rectangle. Take stick of butter and spread evenly over dough. Repeat with both sugars and cinnamon.
Take the edge closest to you and begin to tuck and roll the dough into a log. Using a serrated knife, slice equal portions, making 12 cinnamon rolls. Place in baking dish, allotting 2-3 inches between each.
For Overnight Cinnamon Rolls
Wrap the prepared baking dish in plastic wrap and place in fridge overnight. The next morning, turn oven on warm setting. Take cinnamon rolls out of the fridge and place on counter and unwrap. Bring a small saucepan to a rolling boil and place on bottom rack of oven, placing cinnamon rolls on top rack. Allow to steam in oven for 30 minutes. After 30 minutes have passed, remove water and cinnamon rolls. Preheat oven to 350 degrees. Return cinnamon rolls to oven for 20-25 minutes, or until tops are slightly golden.
For Same Day Cinnamon Rolls
Once cinnamon rolls have been placed in baking dish, cover with a clean towel and let rest in a dry/warm area for 30 minutes. Preheat the oven to 350 degrees. Cook for 20-25 minutes, or until tops are slightly golden
Combine the butter, room temperature cream cheese, salt, and vanilla bean paste. Whisk on high speed for three minutes. Add the powdered sugar, whisking another three minutes. Icing can be made ahead and stored at room temperature.