Preheat your oven to 325°F (163°C). Grease the sides of a 9-inch springform pan.
In a medium bowl, combine graham cracker crumbs, melted butter, and granulated sugar. Mix until well combined.
Press the mixture firmly into the bottom of the prepared springform pan to create the crust. Set aside.
In a large mixing bowl, beat the softened cream cheese with an electric mixer until smooth and creamy. Scrape the sides of the bowl as needed.
Gradually add the granulated sugar, vanilla extract, and peppermint extract to the cream cheese. Mix until well combined.
Add the eggs, one at a time, mixing well after each addition. Mix in the sour cream until smooth.
Finally, add the flour and mix until just combined.
Pour the filling over the prepared crust in the springform pan and smooth the top with a rubber spatula.
Bake in the preheated oven for about 60 minutes, or until the edges are set and the center is slightly jiggly.
Turn off the oven and crack the oven door, letting the cheesecake cool in the oven for 1 hour.
Remove the cheesecake from the oven and refrigerate it for at least 4 hours, or preferably overnight.
Before serving, garnish with crushed peppermint candies on top.