Preheat oven to 325°F (160°C). Mix graham cracker crumbs, sugar, and melted butter. Press into the bottom of a 9-inch springform pan. Bake for 10 minutes, then cool.
Beat cream cheese and sugar until smooth. Add eggs one at a time, then mix in sour cream and vanilla. Pour over crust.
Place the pan on the center rack. Bake for 50–60 minutes, until edges are set but center still jiggles slightly. Turn off oven, crack the door, and let cheesecake rest inside for 1 hour.
Remove, cover, and refrigerate at least 4 hours or overnight.
In a saucepan, combine cranberries, sugar, and water. Simmer 10 minutes until berries burst. Stir in cornstarch slurry to thicken. Cool completely.
Spread cranberry topping over chilled cheesecake before serving.
Notes
For a lighter option, use low-fat cream cheese and sour cream.
Cheesecake can be made 1 day in advance; keep refrigerated until serving.
Cranberry topping can be swapped with raspberry or cherry sauce if preferred.