Add warm milk, sugar, and instant yeast to the bowl of a stand mixer. Gently stir then let it sit for 5-10 minutes, until the yeast begins to grow.
Add eggs, sugar, and melted butter to the bowl. Mix until everything is combined. Add flour and salt and mix again. Let the dough mix for 2 minutes. If the dough is very sticky, add 1 tbsp additions of flour until it is no longer really sticky. The dough should be very soft, but not very sticky.
Let the dough mix for another 2-3 minutes, about 5 minutes total. Cover the bowl and put it in a warm place to rise for 1 hour, or until it has doubled in size. **if you want to split up this process overnight, see my paragraph above the recipe for overnight instructions.
While the dough rises, prep the brown butter. Add 10 tbsp of butter (enough for the filling and icing) to a pan over medium heat. Continuously stir while the butter melts. After a couple minutes the butter will begin to bubble. Keep stirring. After a couple more minutes, the butter will foam up. When the foaming subsides, you'll be left with brown, nutty smelling butter! Take the pan off the heat and pour the brown butter into a bowl. We need the butter to cool down, so put cover the bowl and put it in the fridge for 30 min or freezer for 15 min.
Turn the dough out onto a lightly floured surface. The dough should be soft and easy to work with. Shape it into a rectangle, then use a rolling pin to roll it out into a 12"x18" rectangle. The brown butter should be cooled, but spreadable. Add 6 tbsp of the brown butter on top of the rolled out dough. Spread the butter evenly across the dough, nearly to the edges. Add the brown sugar and cinnamon and evenly spread it as well.
If you are adding bananas and walnuts, add them now. Place the thin slices of banana about 1.5-2 inches apart, in about 6 rows. Sprinkle the walnut chunks evenly over the dough.
Starting on the long end, roll up the dough. Roll it up tightly, but not so tight that you're stretching the dough. Using a ruler or measuring tape, make small notches in the rolled up dough, every 1.5 inches apart, so you'll have evenly sized rolls. Using a very sharp knife, or unscented dental floss, cut the dough along those notches. You should have 12 rolls.
Transfer the rolls to a greased or lined 9x13" pan. Cover and let them rise for 30-60 minutes.
When the rolls are almost done rising, preheat the oven to 350 F. Bake for 18-20 minutes, until the rolls are golden brown.
While the rolls are baking, make the icing. Add the cream cheese and the remaining brown butter (4 tbsp) to a large bowl or stand mixer. Mix for 2 minutes, until completely combined and fluffier. Add the powdered sugar and vanilla, and mix another 2 minutes. The icing should be smooth and creamy.
Once the rolls have cooled for 5-10 minutes, spread the icing on the warm rolls. Enjoy!
If you have any leftover, keep them in a sealed container. They will stay good for 4-5 days.