Preheat oven to 350°.
In a small bowl, add the cream cheese and 1/4 cup of brown sugar. Mix together until well combined. Set in the refrigerator until ready to use.
In a small saucepan, melt the butter over medium heat. Add the rest of the brown sugar (1 3/4 C) and mix well. Bring to a light boil for about a minute. Pour 1/3 of the mixture on the bottom of a well-greased bundt pan.
Remove the cream cheese mixture from the refrigerator. Take each roll and slightly flatten, pulling with your fingers to spread it out a little bit. Place about 1 Tbsp of the cream cheese mixture in to the middle and then fold the dough around the mixture, rolling the dough into a ball with the cream cheese completely enveloped in the middle.
Place 10 of the rolls in the bundt pan and sprinkle with half of the cinnamon sugar. Pour another third of the brown sugar/butter mixture on top of that layer. Add the other 10 rolls, then the rest of the cinnamon sugar mixture and then the rest of the brown sugar/butter on top.
Let rise for about 30 minutes to an hour and then bake for 50-60 minutes. After about 35-40 minutes, you will need to place a piece of foil on top of the bundt pan to prevent the rolls from getting too brown. The easiest way to tell if the rolls are done in the middle is to use a thermometer. Once the internal temperature of the rolls is 190° F, the rolls are completely cooked through.
Immediately invert the bundt pan onto a plate and remove the pan. Just like all cinnamon rolls, these taste the best when fresh and warm!