In the microwave or on the stove melt butter with the milk. Melt just until the butter is melted and the mixture is warm but not hot. (Let sit if needed.)
In a separate large bowl, whisk together 3 cups flour, sugar, and salt until combined.
In the bowl of a stand mixer with the dough hook attachment, add the instant yeast and lukewarm milk mixture and stir to combine.
Add the flour mixture and egg, then beat on medium-low speed until combined.
If the dough is still sticking to the sides of the bowl gradually add the remaining flour until it pulls away from the sides of the bowl. The dough should be a smooth elastic ball and tacky to the touch.
Knead with the dough hook for 5 minutes on medium-low speed.
Transfer the dough to a large, lightly greased bowl, cover the bowl with a damp towel and let rest for 10 minutes.
Roll each portion of dough into a 16-inch by 11-inch rectangle. Spread softened butter over the rectangle.
Stir together the cinnamon sugar filling. Then sprinkle and spread it evenly over the rectangle.
Starting at one long side tightly roll up the dough, and pinch the seal tightly.
Cut the log into 12 equal pieces and place them into a greased 9x13 baking dish.
Cover with greased plastic wrap and let rise for 25 minutes.
Preheat oven to 350 degrees, uncover the rolls and bake for 15-20 minutes or until the rolls are golden.
Let cool on a wire rack for at least 5 minutes.
For the frosting, in a large bowl, whip together the cream cheese and butter. Add the vanilla, maple and salt and mix until combined.
Gradually add the powdered sugar and mix until thick and creamy. Add cream or milk a tablespoon at a time until the frosting is smooth.
Spread frosting on cinnamon rolls and enjoy!
Cover cinnamon rolls to store.