Before getting started, be sure that the cream cheese is very soft and the sour cream is room temperature. That’s the best way to insure that you get a smooth, even cheesecake with no cracks or lumps.
Preheat oven to 325F degrees.
Line a mini muffin tin with liners. (Note: You can use nonstick cooking spray instead of muffin liners, but the muffin liners make these much easier to remove from the pan.)
In the bowl of a food processor, pulse together the graham crackers, melted butter, and ½ tsp sugar until the mixture resembles wet sand. Divide crust between spaces in the mini muffin tin and gently press it down using the back of a spoon or your fingers. You should just have a thin layer of crust in each tin.
Wipe out the bowl of the food processor and then combine cream cheese, sour cream, and ½ cup sugar in the food processor. Blend until very smooth. Add egg and vanilla and blend just until the egg is fully incorporated (don’t overmix once the egg has been added or you will get light and fluffy, rather than creamy cheesecakes).
Spoon cheesecake filling over the crusts, filling each space to just below the top.
Bake until the cheesecakes are set and the edges are just barely beginning to brown, 15 to 18 minutes.
Allow cheesecakes to cool completely in the pan.
Refrigerate cheesecakes before serving. (They can be made up to 4 days ahead and stored in an airtight container in the fridge.)