01 - Preheat the oven to 325°F. Line a 12-cup muffin tin with paper liners.
02 - In a medium mixing bowl, blend graham cracker crumbs, granulated sugar, and melted butter until the mixture is evenly moistened. Distribute the crumb mixture among the muffin liners and press firmly to create a compact base.
03 - In a clean mixing bowl, beat cream cheese and granulated sugar with an electric mixer until smooth. Incorporate egg, vanilla extract, and sour cream, mixing just until combined. Spoon the cheesecake filling evenly over the prepared crusts.
04 - Bake in the preheated oven for 16 to 18 minutes or until the centers are just set. Allow to cool at room temperature for 30 minutes, then refrigerate for at least 1 hour.
05 - In a small saucepan over medium heat, combine brown sugar, unsalted butter, heavy cream, and salt. Stir continuously until the mixture comes to a simmer and thickens, about 3 to 4 minutes. Remove from heat, stir in chopped pecans and vanilla extract, and allow to cool slightly.
06 - Once the cheesecakes are fully chilled, spoon pecan topping over each mini cheesecake. Chill for an additional 15 to 20 minutes before serving.