Prepare a 6 quart Crock-Pot slow cooker by lining the inside with a large sheet of parchment paper. Press it into the corners to fit it into the ceramic insert and to cover the entire interior surface and sides of the pot. Set aside.
To make the dough
Place the flour, sugar, and fine kosher salt in a stand mixer fitted with the paddle attachment. Stir them together for a few seconds on low just to get everything evenly mixed.
In a small bowl, place the warm water (the temperature of the water should be around 38–40 ºC or 100 ºF). Stir in the ½ teaspoon of sugar and sprinkle the yeast over top. Stir everything together and let rest for 10 minutes. The mixture should develop a thick foam on top.
Meanwhile combine the milk with the butter in a microwave-safe bowl and heat it in the microwave for a minute or so, just enough to melt the butter. Let stand at room temperature to cool slightly.
When all the components are ready, add the milk and butter mixture to the mixer, along with the foamy yeast mixture and the two eggs. Stir them together on low speed to form a shaggy, evenly mixed dough.
Switch to the hook attachment to begin kneading on low speed. If the dough seems too wet, add up to 30 grams (¼ cup) of all purpose flour. The dough should not be so sticky and it shouldn't stick to the bowl. It should feel tacky.
Knead the dough for 8 minutes, then dump it out on the counter and knead it by hand for a minute or so to form a smooth round ball of dough.
Place a towel over the dough and let it rest for 10 minutes while you prepare the filling.
To make the filling
In a bowl, cream together the softened butter, the sugars, and the cinnamon until you have a thick brown paste. Set aside.
Assemble the rolls
When the dough has rested, remove the towel and roll it out on a very lightly floured surface to a big rectangle of at least 9x15 (don't worry too much if it's bigger).
Spread the filling over the entire surface of the dough, then roll tightly into a 15 inch log.
Cut the dough into 12 equal buns (you don't have to trim the ends) and place them in the prepared ceramic insert.
Bake the rolls
Place the ceramic insert in the Crock-Pot base.
Wrap the lid in a kitchen linen or two to absorb any moisture that is released during the bake. Place the lid over the ceramic insert and make sure it's on tight.
Plug in the Crock-Pot and set it to cook on high for 2 hours.
After 1 hour of cooking, lift the ceramic up and rotate the pan, setting it back down in the base.
After another 30 minutes, using a digital thermometer, check the temperature of the bready part of a middle bun to make sure it's reached 93 ºC or 200 ºF. Once the bread hits that temperature, the buns are done baking.
Using oven mitts, lift the ceramic insert out of the base. Remove the lid and using the parchment, lift the buns out of the ceramic pot, setting the parchment-lined buns on a cooling rack while you prepare the icing. Let them cool 10 minutes before icing them so that the icing doesn't melt and run off the buns.
Make the frosting
Cream together the cream cheese, icing sugar, milk, and vanilla bean paste.
Using an offset spatula (or the back of a spoon), spread the frosting on the top of the buns. Serve warm