Add the butter to a saucepan set over medium heat, occasionally stirring. Continue occasionally stirring the mixture until it turns amber in color and develops little brown specks (those are the toasted milk solids - the flavor!)
Remove the butter from the heat and set aside. You should be left with 90g (~6 ½ tbsp.), which will be distributed throughout the dough, filling, and frosting.
Tangzhong
In a small saucepan over medium heat, continuously stir together the flour and milk until the mixture and thickens into a thick slurry. Take off the heat and set aside. Alternatively, whisk together the flour and milk in a microwave safe bowl. Microwave in 30 second intervals, stirring after each, until the mixture becomes a thick slurry.
Dough
Add all of the ingredients, including the tangzhong and 42g of brown butter into the bowl of a stand mixer fitted with the dough hook attachment.
Knead the mixture on medium-high speed for ~15-20 minutes. The dough is ready when it is no longer sticking to the sides or bottom of the bowl, and passes the windowpane test.*
Once the dough is done kneading, shape the dough into a ball and place it back into the mixing bowl. Cover the mixing bowl with plastic wrap, and place it in a warm area to rise until doubled in size (~1 hr.)**
Filling
In a small bowl, mix together the brown sugar and cinnamon and set aside.
Once the dough has finished rising, lightly punch it down to remove any excess air in it. Transfer the dough to a clean and lightly floured surface, then roll it out to a 12″ x 16″ (30 x 40 cm) rectangle. If the dough keeps springing back a lot while rolling it out, let it rest for 5 minutes before continuing.
Carefully spread 3 tbsp. of the brown butter over the dough (you may have to melt it a little if it's hardened), then sprinkle the cinnamon sugar over the butter in an even layer. From the longer side, roll up the dough into a tight long. Use a sharp knife or floss to cut the dough into 6 even pieces.
Transfer the rolls to a lightly buttered and/or lined eighth sheet pan*** Lightly cover the pan with a towel, and let the rolls rise in a warm environment until doubled in size (~30 minutes).
Preheat the oven to 350°F / 175°C.
(Optional, for browning) Make an egg wash by whisking together an egg with 1 tbsp. milk, then brush it over the rolls.
Bake for ~20 minutes, until the tops of the rolls are golden brown and the internal temperature of the rolls has reached 180°F / 82°C.
Cream Cheese Frosting
In a small bowl, beat together the cream cheese, brown butter, and sugar until smooth. Then beat in the heavy whipping cream until well combined.
Spread the frosting over the warm rolls, then serve and enjoy!
Notes
*Take a small piece of dough and stretch it gently as far as you can. If it tears super easily, keep kneading. If it's able to spread to the point where it's super thin and you can see light through it, it has passed the windowpane test and is good to go!**At this point you could leave the dough in the fridge overnight, and proceed with the rest of the recipe the next day.***An eighth sheet pan is 10x7". You could also use an 8" circle pan, or you could cut the dough into 9 strips and use an 8" square pan.