If using a stand mixer, add all dough ingredients to the work bowl. Use the dough hook attachment and knead for 7 to 10 minutes, until the dough is smooth and pulls away from the sides.
If mixing by hand, knead the dough for 7 to 10 minutes using the palms of your hands.
Cover the bowl with a damp towel and allow the dough to rise in a warm place for 1 hour and 15 minutes.
Punch down the risen dough and roll it out on a lightly floured surface to form a 16 by 10 inch rectangle.
Line two 9×13 pans with parchment paper. Melt the 1/2 cup butter for the brown sugar base.
Pour half of the melted butter and half of the brown sugar evenly into each prepared pan.
In a small bowl, mix the soft butter, brown sugar, and cinnamon for the filling. Spread this mixture evenly over the rolled-out dough.
Starting from the long edge, roll the dough into a tight log. Cut the log into 12 equal rolls using a sharp knife or dental floss.
Place 6 rolls in each prepared pan on top of the brown sugar and butter mixture.
Bake for 25 to 30 minutes or until the rolls are golden brown and puffed. Let cool slightly in the pan before adding sauce.
In a saucepan, combine the brown sugar and heavy cream over medium heat. Bring to a simmer and stir until the sugar dissolves.
Add the soft cream cheese and whisk until the sauce is smooth and creamy.
Drizzle the warm rolls generously with the cream cheese toffee sauce before serving. Enjoy warm.