To make the dough. Place the yeast and 1 tablespoon brown sugar into a stand mixer with the dough hook attached. Add the warm water and gently stir. Let sit until yeast has doubled and is puffed and foamy on top, about 10 minutes. To the bowl add the melted butter, warm milk and egg, stir to combine. Add in the flour and salt. Knead the dough with the dough hook until the dough is smooth and forms a ball, about 5 minutes. Remove the dough from the bowl and oil the bowl or use cooking spray. Place the dough back into the bowl and cover with plastic wrap. Let the dough rise in a warm area for about 1 hour or until doubled in size.
Meanwhile, make the filling. Heat a large skillet over medium heat and add 1 tablespoon butter. Add the apples and 2 tablespoons brown sugar. Cook, stirring often until the apples are caramelized, about 5 minutes. Remove from the heat and let cool.
Add the sugar and cinnamon to a bowl and mix well.
Generously grease a 9×13 inch baking dish with butter.
Lightly dust a surface with flour. Roll the dough into a rectangle (about 9×24 inches). Spread the 5 tablespoons of butter evenly over the dough. Sprinkle the cinnamon sugar evenly over the butter and lightly push the cinnamon sugar into the butter. Evenly sprinkle the apples over the dough. Starting with the long edge closest to you, carefully roll the dough into a log, keeping it fairly tight as you go. When you reach the edge, pinch along the edge to seal. Place dental floss or a thin piece of string (do it, it works so well!) under the roll where you want to cut. Mine are usually about 3/4 to 1 inch thick, but vary. Take the ends of the floss in each hand and wrap them around the roll. Keeping the ends of the floss in each hand (don’t let go) tighten the floss so it starts to cut through the roll. Again, don’t change hands. Tighten until the floss comes out and the individual roll is separated. You can make eight larger rolls OR 10-12 smaller rolls. Place rolls in the prepared pan. Cover with a damp cloth or plastic wrap and allow to rise in a warm place until doubled in size, about 30 minutes. Preheat oven to 350. Just before baking, brush the remaining 2 tablespoons butter on top of the rolls. Bake the rolls for 25 minutes or until golden brown.
Meanwhile, make the frosting. In a medium bowl, beat together the cream cheese, butter and vanilla until fluffy. Add the powdered sugar, cinnamon, all-spice, ginger, and cardamon and beat until combined. Spread the frosting on warm rolls. EAT!