01 - Preheat oven to 325°F. Line a 12-cup muffin tin with paper liners.
02 - Blend graham cracker crumbs, granulated sugar, and melted butter in a medium bowl until evenly combined. Distribute mixture into liners and press firmly to form compact crusts.
03 - Beat cream cheese and sugar until smooth in a mixing bowl. Add the egg, vanilla extract, and sour cream; mix until just blended. Spoon evenly over each crust.
04 - Bake for 16 to 18 minutes, or until centers are just set. Cool at room temperature for 30 minutes, then chill in the refrigerator for at least 1 hour.
05 - In a small saucepan over medium heat, combine brown sugar, butter, heavy cream, and salt. Bring to a simmer, stirring constantly, until thickened, about 3 to 4 minutes. Remove from heat, stir in chopped pecans and vanilla extract, and let cool slightly.
06 - Top each chilled mini cheesecake with pecan mixture. Refrigerate for another 15 to 20 minutes before serving.