Preheat oven to 350°F (175°C). Grease and flour a 9-inch springform pan.
In a medium bowl, combine graham cracker crumbs, 0.375 cup granulated sugar, and melted butter. Press evenly into the bottom of the prepared springform pan.
In a large bowl, beat cream cheese and 1 cup granulated sugar until smooth. Beat in eggs one at a time, then stir in vanilla extract and sour cream.
Pour half of the cream cheese mixture over the crust.
In a small bowl, combine brown sugar and cinnamon. Sprinkle half of this mixture over the cream cheese layer. Drizzle with half of the melted butter.
Pour the remaining cream cheese mixture over the cinnamon layer. Sprinkle with the remaining brown sugar and cinnamon mixture. Drizzle with the remaining melted butter.
Bake for 55-65 minutes, or until the edges are set and the center is still slightly jiggly. Turn off the oven, crack the door open, and let the cheesecake cool in the oven for 1 hour.
Remove from oven and let cool completely on a wire rack. Chill in the refrigerator for at least 4 hours, or preferably overnight.
While the cheesecake is chilling, prepare the glaze. In a medium bowl, beat cream cheese until smooth. Gradually beat in powdered sugar, milk, and vanilla extract until well combined and smooth.
Once the cheesecake is chilled, drizzle the glaze over the top before serving.
Notes
For an extra festive touch, sprinkle chopped pecans or walnuts over the cinnamon swirl before baking.