01 - Preheat oven to 325°F (165°C). 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 evenly moistened. Divide the mixture among muffin liners, pressing firmly into an even base in each well.
03 - In a mixing bowl, beat softened cream cheese with granulated sugar until completely smooth. Add egg, vanilla extract, and sour cream; mix until just incorporated without overbeating.
04 - Spoon the cheesecake filling over prepared crusts, dividing evenly. Bake for 16 to 18 minutes, or until centers are just set. Remove from oven and allow to cool at room temperature for 30 minutes.
05 - Transfer cheesecakes to the refrigerator and chill for at least 1 hour to fully set.
06 - In a small saucepan over medium heat, combine brown sugar, unsalted butter, heavy cream, and salt. Stir constantly until the mixture simmers and thickens, about 3 to 4 minutes. Remove from heat, stir in chopped pecans and vanilla extract, then allow to cool briefly.
07 - Once cheesecakes are thoroughly chilled, spoon pecan topping onto each. Chill for an additional 15 to 20 minutes before serving.