In the bowl of a stand mixer, combine the all purpose flour, bread flour, yeast, salt, sugar, milk, and eggs.
Fit the dough hook attachment to the mixer. Miix the ingredients on low speed for 3-4 minutes until the ingredients are thoroughly combined, and pockets of dry flour have been fully incorporated.
Mix for an additional 3-4 minutes. The dough will be stiff and dry.
Add the butter, a piece at a time, mixing after each addition until each piece is mixed into the dough.
Mix on low speed for 10 minutes, stopping to scrape down the bowl every so often to fully incorporate the butter. The dough will look like a gooey mess, but that's ok.
Once the butter has been completely incorporated, increase the mixer speed to medium and beat for 15-18 minutes. The dough will go from gooey and shaggy to smooth and cohesive.
Turn up the speed to medium high and beat for 2 minutes. You should hear the dough making a slapping sound against the sides of the bowl.
The dough should have a little bit of stretch and should be able to be picked up in one piece. If the dough breaks when you pull at it, mix on medium speed for an additional 2-3 minutes.
Cover the bowl with plastic wrap, pressing the plastic wrap against the surface of the dough so that it doesn't form a skin.
Proof the dough in the fridge overnight.
In the morning, remove the dough from the fridge and set aside so you can prepare the cinnamon sugar filling.
Combine the softened butter, brown sugar, salt and cinnamon in a small bowl and mix into a smooth paste. Set aside.
On a floured surface, roll out the dough to a 18x12 rectangle.
Make sure the long side is facing you. Starting on the long side of the dough closest to you, tightly roll up the dough into a log. Pinch the seams together so that the log doesn't become unrolled when cutting into rolls.
Trim 1/4" off of each end of the log. Cut the dough using a sharp knife, a bench scraper, or unflavored dental floss into rolls, about 1 1/2" wide.
Line a 9x13 baking pan with parchment paper. Place the rolls evenly in the pan, leaving space between each roll.
Cover the pan with plastic wrap and proof in a warm spot for two hours, until the dough has risen, is puffy and the rolls are touching each other.
Heat the oven to 350F. Remove the plastic wrap from the rolls. Bake for 35-40 minutes, or until the internal temperature of the rolls reaches 190F.
While the rolls are baking, make the frosting. Place the butter in a light-colored sauce pan over medium-low heat. Once melted, the butter will begin to pop and sizzle around the edges. In about 5-8 minutes from when you started, the butter will turn dark golden brown. The majority of the popping will subside and the milk solids at the bottom of the pan will be a dark toasty brown. It will smell buttery and nutty, but not burned. Let the butter cool to room temperature.
In the bowl of a stand mixer, combine the cream cheese, confectioners sugar, salt and vanilla. Add in the room temperature browned butter and mix to combine. When all the ingredients are combined, turn the speed up to medium. Whip until light and fluffy, about 3-4 minutes.
Once the rolls are out of the oven, let them cool for about 5 minutes before adding the frosting. Spread the frosting over the warm rolls and serve.