Melt butter in a small saucepan over medium heat. Stir in brown sugar and cook for about 3 minutes, stirring constantly.
Remove saucepan from heat and stir in whipping cream. Return to heat and bring to a boil while continuing to stir. Once boiling reduce heat to medium and stir until thickened, about 5 minutes.
Remove from heat and stir in rum extract. Pour mixture into a greased 9-inch pie plate. Set aside.
Mix brown sugar and cinnamon in a small bowl.
Separate the crescent roll dough into eight rectangles. Sprinkle brown sugar and cinnamon evenly over each piece of dough. Roll up dough starting on the shorter side.
Cut dough into one-inch pieces. Place rolls in the prepared dish.
Bake for 18 minutes or until golden brown.
Remove from oven and let cool a minute or two before flipping onto a plate. Serve hot.