01 - Preheat oven to 325°F. Line a standard 12-cup muffin tin with paper liners.
02 - In a medium mixing bowl, combine graham cracker crumbs, granulated sugar, and melted butter. Stir until the mixture resembles wet sand. Evenly divide among muffin liners, pressing each portion firmly to form a compact base.
03 - Using an electric mixer, beat the softened cream cheese and granulated sugar until smooth and creamy. Add egg, vanilla extract, and sour cream; continue mixing on low speed until just incorporated to avoid overbeating.
04 - Spoon the cheesecake batter evenly over prepared crusts in the muffin tin. Bake in the preheated oven for 16 to 18 minutes, until centers are just set. Remove from oven and allow to cool at room temperature for 30 minutes. Transfer to refrigerator and chill for at least 1 hour.
05 - While cheesecakes chill, combine brown sugar, butter, heavy cream, and salt in a small saucepan over medium heat. Simmer and stir constantly until the mixture thickens, about 3 to 4 minutes. Remove from heat, stir in chopped pecans and vanilla extract, and let cool slightly.
06 - Spoon the cooled pecan topping generously over the chilled cheesecakes. Chill for an additional 15 to 20 minutes before serving.