In a medium saucepan, heat the milk and butter over medium heat until the butter melts and the mixture is warm (but not boiling).

In a large mixing bowl, combine 4 cups of the flour, yeast, sugar, and salt.

Add the slightly beaten egg and the lukewarm milk-butter mixture, mixing until the dough begins to come together.

Gradually add the remaining flour, 1/2 cup at a time, until the dough is soft and pulls away from the sides of the bowl.

Work the dough on a floured surface for approximately 5 to 7 minutes until it reaches a smooth and elastic texture.

Place the dough in a greased bowl, cover with a towel, and let it rise in a warm place for about 1 hour, or until it has doubled in size.

While the dough is rising, if using raisins, soak them in the warm rum for about 30 minutes. Drain and set aside.

In a small bowl, mix together the carrot cake flavored cake mix and cinnamon. Set aside.

Once the dough has risen, punch it down and knead in the finely chopped carrots.

Flatten the dough into a large rectangle, approximately 1/4 inch thick.

Spread the softened butter evenly over the dough, then sprinkle the carrot cake filling mixture over the top.

If using raisins, scatter them evenly across the dough.

Starting from the long side of the dough, tightly roll it into a log.

Slice the log into 12 equal pieces and arrange them in a greased 9x13-inch baking pan.

Cover the dish with a towel and let the rolls rise for another 30 minutes, or until they are puffy.

Preheat the oven to 350°F (175°C).

Bake the rolls for 25 to 30 minutes, or until they achieve a rich golden hue and are thoroughly baked.

Remove from the oven and allow them to cool slightly before frosting.

In a medium bowl, beat the cream cheese and butter together until smooth.

Add the vanilla extract and gradually mix in the powdered sugar until the frosting is thick and creamy.

Spread the cream cheese frosting generously over the warm rolls.

Serve immediately and enjoy the delicious combination of carrot cake and cinnamon roll flavors.