01 - Preheat the oven to 325°F. Line a 12-cup muffin tin with paper liners.
02 - In a medium bowl, combine graham cracker crumbs, granulated sugar, and melted unsalted butter. Mix until fully moistened, then divide the mixture evenly among the paper liners and press firmly to create compact crusts.
03 - In a mixing bowl, beat softened cream cheese and granulated sugar until creamy and smooth. Incorporate the egg, vanilla extract, and sour cream; blend until just combined. Evenly portion the filling over each prepared crust.
04 - Bake in the preheated oven for 16 to 18 minutes, or until the cheesecake centers are nearly set. Cool at room temperature for 30 minutes, then refrigerate for at least 1 hour to ensure a firm texture.
05 - In a small saucepan set over medium heat, combine brown sugar, unsalted butter, heavy cream, and salt. Stir continuously until the mixture thickens and simmers, about 3 to 4 minutes. Remove from heat, add chopped pecans and vanilla extract, and allow to cool briefly.
06 - Once the cheesecakes are well chilled, spoon the pecan topping onto each mini cheesecake. Return to refrigeration for an additional 15 to 20 minutes before serving.