Place an oven rack in the center of the oven and one in the lower third. Fill a large roasting pan halfway with water and place on lower rack. Preheat oven to 325 degrees. Coat a 9-inch springform pan with cooking spray.
Cut each cinnamon roll in half and place them so the cut side (middle of the cinnamon roll) is facing down. They will rise quite a bit so press down on them some and don't put them too close together. Once they are all placed press down on them more to close most of the gaps. It's ok if there are some gaps left. You may not need to use all the cinnamon rolls. Spread icing that comes with cinnamon rolls on top of them.
Make Filling. Beat cream cheese and sugar on medium-high until smooth and fluffy, about 2-3 minutes.
Beat in eggs one at a time, scraping down sides of bowl a few times.
Add sour cream, flour, and vanilla and beat until combined.
Make Brown Sugar Mixture. In a small bowl, combine brown sugar, flour, butter, and cinnamon. Mix with a fork to combine well.
Pour half of cheesecake filling over cinnamon rolls. Scatter brown sugar mixture on top of filling and then pour remaining filling on top. Keep in mind that cinnamon rolls will rise some. You don't want the filling to come all the way to the top, so you may not need to use all of it depending on your pan, the size of your cinnamon rolls, and how many cinnamon rolls you used.
Place on a baking sheet and place in oven on center rack. Bake for 1 hour. Turn oven off. Leave cheesecake in oven with door cracked slightly for 1 hour. Remove cheesecake from oven and let cool to room temperature. Refrigerate over night.
Make Cream Cheese Topping. Beat cream cheese and butter with an electric mixer until smooth. Gradually beat in confectioners' sugar and milk. Spread on top of chilled cheesecake.
Make Cinnamon-Sugar Drizzle. In a small microwave bowl, combine dark brown sugar, butter, and cinnamon. Microwave at 10 second intervals until melted and smooth. Let cool slightly and pour into a plastic sandwich bag, Snip the corner and drizzle on cheesecake in desired pattern.