Preheat your oven to 350°F (175°C). Lightly grease a standard 8-cup or 12-cup muffin tin with non-stick cooking spray to ensure the cups are easy to remove after baking.
Open the cinnamon roll package and separate the individual rolls. Place one roll into each prepared muffin cup. Use your fingers or the back of a small spoon to press the dough down and slightly up the sides, creating a small well for the filling.
In a medium mixing bowl, combine the softened cream cheese and granulated sugar. Beat with a hand mixer until the mixture is smooth and creamy. Add the egg and vanilla extract, then continue to mix until just combined. Be careful not to overbeat once the egg is added.
Spoon the cheesecake mixture evenly into the center of each cinnamon roll cup. Each one should be filled about three-quarters of the way to the top, as the cheesecake will puff up slightly during baking.
Place the muffin tin in the oven and bake for 18 to 22 minutes. The edges of the cinnamon rolls should be golden brown, and the cheesecake centers should be set but still have a very slight jiggle in the middle.
Remove the tin from the oven and let the dessert cups cool for at least 10 minutes. Once cooled, drizzle the reserved icing from the package over the top of each cup for a sweet finish.