Preheat your oven to 325°F (160°C). In a medium mixing bowl, use an electric mixer to beat the softened cream cheese until it’s completely smooth and creamy. Gradually add in the granulated sugar and vanilla extract, mixing until the ingredients are fully combined and fluffy.
One by one, add the eggs to the cream cheese mixture, ensuring that you mix thoroughly after each addition to maintain a smooth texture. Finally, sift in the flour and gently fold it in until just combined. Set this mixture aside.
In a separate bowl, combine the packed brown sugar and ground cinnamon. Gradually pour in the melted butter, stirring continuously until the mixture is well blended. Slowly add the flour and mix until the mixture reaches a crumbly consistency and resembles streusel.
Lightly grease a 9-inch springform pan. Pour half of the cheesecake batter into the pan and spread it evenly. Next, sprinkle half of the cinnamon roll filling over the cheesecake layer. Gently pour the remaining cheesecake batter on top, followed by the rest of the cinnamon roll filling. Use a butter knife to swirl the layers together for a lovely marbled effect.
Place the pan in the center of the preheated oven and bake for approximately 50-60 minutes. The cheesecake should be set around the edges but still slightly jiggly in the center. When the time is up, turn off the oven and leave the cheesecake inside for an additional hour to cool gradually.
After an hour, take the cheesecake out of the oven and allow it to cool at room temperature for 30 minutes. Once cooled, cover and transfer it to the refrigerator to chill for at least 4 hours, although overnight is preferable for the best texture.
In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until the mixture becomes smooth and drizzleable. If you'd like a thinner glaze, slowly add more milk until desired consistency is achieved.
When ready to serve, remove the cheesecake from the refrigerator and drizzle the glaze over the top. Carefully detach the sides of the springform pan for a beautiful presentation.