Preheat oven to 350°F (175°C). Grease and flour a 9-inch springform pan.
In a medium bowl, combine graham cracker crumbs, melted butter, and 0.25 cup granulated sugar. Press firmly into the bottom of the prepared pan.
In a small bowl, mix together the brown sugar and cinnamon. Cut in the softened butter until crumbly.
In a large bowl, beat cream cheese and 1.5 cups granulated sugar until smooth. Beat in eggs one at a time, then stir in vanilla extract and sour cream.
Pour half of the cheesecake filling over the crust. Sprinkle half of the cinnamon mixture over the filling. Dollop the remaining filling over the cinnamon mixture and sprinkle with the remaining cinnamon mixture.
Gently swirl the cinnamon mixture into the cheesecake batter with a knife or toothpick.
Bake for 55-65 minutes, or until the center is almost set but 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 cool completely on a wire rack. Refrigerate for at least 4 hours, or preferably overnight, before serving.
Notes
For a smoother swirl, you can melt the butter for the cinnamon mixture slightly.