Preheat the oven to 350°F. Grease a 9-inch springform pan.
Mix together the graham cracker crumbs and sugar in a medium bowl. Add the melted butter and stir until well combined. Press the mixture into the bottom of the prepared pan.
Bake the crust for 10 minutes. Remove from oven and let cool completely.
Lower the oven temperature to 325°F.
Using an electric mixer, beat the cream cheese until smooth and creamy.
Add the sugar and vanilla extract, and beat again until combined.
Add the eggs, one at a time, beating well after each addition. Pour the mixture over the cooled crust and smooth the top with a spatula.
Bake for 45-50 minutes, or until the edges are set and the center is slightly jiggly.
Let the cheesecake cool to room temperature before refrigerating for at least 4 hours, or overnight.
To make the candied pecans topping, melt the brown sugar and butter in a small saucepan over medium heat. Add the pecans and stir until coated. Cook for an additional 2-3 minutes, stirring constantly. Remove from heat and stir in the vanilla extract.
Top the chilled cheesecake with the candied pecans and serve.