Preheat the oven to 375°F. Grease a 12-cup muffin tin with baking spray. Set the muffin tin on top of a large rimmed baking sheet, or add a large piece of aluminum foil to the bottom rack of the oven to catch any drippings from the muffins.
Separate the cinnamon rolls and cut each one into 6 equal pieces. Set aside.
In a gallon-sized zipper plastic bag, add 2/3 cup brown sugar and the cinnamon. Close the bag securely then toss to combine. Add the cinnamon roll pieces, then close the bag and toss until the cinnamon roll pieces are evenly coated. Place 8 pieces of the rolls into each muffin tin, pressing down slightly.
In a small saucepan combine the butter and 1/2 cup brown sugar. Bring to a boil over medium low heat, stirring constantly. Remove from the heat, then drizzle the glaze evenly over each muffin in the tin.
Bake the muffins for 14-16 minutes until the glaze is bubbly and the tops of the muffins are browned and crisp. *The glaze may overflow the pan. This is why you need to add a large rimmed baking sheet underneath the muffin tin or place a large piece of foil on the rack below in the oven.
Let the muffins cool in the tin for 5-8 minutes. Take the muffins out by running a butter knife around the perimeter and scooping them out underneath. Place on a wire rack to cool.
While the muffins cool, make the icing by beating the softened cream cheese in a small bowl. Add the powdered sugar and mix it in until smooth. Add the vanilla and the milk, starting with 1 tablespoon of the milk, and mix until smooth. The mixture should be thick but pourable. Add more milk a little bit at a time if needed.
Drizzle the icing over the muffins and serve warm or at room temperature.