Preheat the oven to 350°F (175°C). Grease a 9-inch springform pan.
Unroll the cinnamon roll dough and place it in the bottom of the springform pan, pressing the dough to form a crust. Bake for 10 minutes, then remove from the oven and let it cool.
In a large mixing bowl, beat the cream cheese with granulated sugar until smooth and creamy. Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract and sour cream until smooth.
Pour the cheesecake filling over the cooled cinnamon roll crust, smoothing the top with a spatula.
Bake the cheesecake for 50-60 minutes, or until the center is set and the top is lightly golden. Turn off the oven, crack the oven door, and let the cheesecake cool for 1 hour.
After cooling, transfer the cheesecake to the refrigerator and chill for at least 2 hours, or overnight.
While the cheesecake is chilling, prepare the cream cheese icing by beating together softened cream cheese, butter, powdered sugar, vanilla extract, and milk until smooth and creamy.
Once the cheesecake has chilled, remove the springform pan and transfer the cheesecake to a serving platter. Drizzle the cream cheese icing over the top.
Slice, serve, and enjoy!