Preheat the oven to 350 degrees F (175 degrees C).
Stir crushed shortbread cookies, melted butter, sugar, and cinnamon for crust together in a medium bowl. Press crumb mixture firmly onto the bottom of a 9-inch springform pan.
Bake in the preheated oven until edges begin to brown and cinnamon is aromatic, 10 to 12 minutes. Let cool on a wire rack for 1 hour. Reduce the oven temperature to 300 degrees F (150 degrees C).
Stir 2 tablespoons sugar and 1 1/2 teaspoon cinnamon for filling together in a small bowl. Set aside.
Beat cream cheese, 1 cup sugar, and sour cream together in the bowl of a stand mixer fitted with a paddle attachment until fluffy, about 3 minutes, scraping down sides of bowl as needed. Add vanilla, remaining 1 teaspoon cinnamon, and salt; continue beating just until combined. Add eggs, one at a time, beating on low just until incorporated, about 1 minute; do not overbeat.
Wrap foil loosely around the bottom and up the sides of the springform pan. Pour the cheesecake batter into the cooled crust and set it in a large baking dish or roasting pan. Pour hot water into the roasting pan to reach halfway up the sides of the springform pan.
Bake on the middle rack of the preheated oven for 60 minutes. Without removing the roasting rack from the oven, carefully slide the oven rack out enough so you can evenly sprinkle cinnamon-sugar mixture over the top of the cheesecake. Carefully slide the oven rack back into the oven and continue baking until the filling is set around the edges and slightly wobbly in center, 10 to 15 minutes more.
Carefully remove from oven. Lift springform pan from roasting pan and place on a wire rack. Let cool to room temperature, about 2 hours. Remove and discard foil from springform pan and place cheesecake in the refrigerator to chill for at least 4 hours or overnight.
Run a hot knife or offset spatula around rim of pan to loosen cake. Remove sides of springform pan. Slice and serve.
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