In a medium bowl, combine the graham cracker crumbs and melted butter. Mix until the crumbs are evenly coated. Press the mixture firmly into the bottom of a 9-inch springform pan to form the crust. Refrigerate for 30 minutes to set.
In a large mixing bowl, beat the softened cream cheese with an electric mixer until smooth and creamy.
Gradually add the powdered sugar, mixing until well combined.
Add the sour cream, key lime juice, lime zest, and vanilla extract. Beat until the mixture is smooth and creamy, scraping down the sides of the bowl as needed.
Pour the cheesecake filling over the chilled crust and spread it evenly.
Cover the cheesecake with plastic wrap and refrigerate for at least 4 hours, or overnight for best results.
Before serving, top with whipped cream and garnish with lime slices if desired.