Preheat the oven to 350°. Open the cinnamon roll tubes and remove the frosting cups; set them aside to come to room temperature. Separate the dough into individual cinnamon rolls and cut each roll into 6 pieces. In a large mixing bowl, combine the granulated sugar and cinnamon. Set aside. In a small saucepan, melt the butter over medium heat. After it is melted, continue to cook it for an additional 3 to 5 minutes, or until the foam and butter underneath are golden brown. Remove from the heat and add the vanilla (it will bubble up!). Once the bubbles have subsided, whisk in the brown sugar until smooth and well combined. Meanwhile, thoroughly spray a 12-cup nonstick Bundt pan with nonstick cooking spray. Add half of the cinnamon roll pieces to the mixing bowl with the cinnamon-sugar mixture. Toss well to coat the pieces. Place the pieces in the Bundt pan, creating an even layer. Drizzle with half of the butter-brown sugar mixture. Repeat tossing and layering with remaining ingredients, stirring butter-brown sugar mixture before drizzling, if needed. Bake for 35 to 40 minutes, until the monkey bread has puffed up about 1 inch in the pan and the top is deep brown. Let cool for 10 minutes in the pan, then place a dinner plate over the top of the pan. With oven mitts, hold the pan and dinner plate together, then flip over. Carefully remove the bundt pan (give it a few taps if the bread doesn't seem to be releasing) and let it slide out onto the plate. Meanwhile, mix the cream cheese with a small rubber spatula until very smooth. Add in the contents of the frosting cups, whisking well to combine. Dollop the icing all over the top of the monkey bread, letting it melt into the top and drizzle down the sides. Serve immediately.