Preheat the oven to 350°F. Line a 12-cup muffin pan with cupcake liners.
Make the crust: in a medium bowl combine 1 1/2 cups graham cracker crumbs, 5 tablespoons unsalted butter (melted), and 1 1/2 tablespoons granulated sugar.
Divide the crumb mixture among the lined muffin cups and press about 1 1/2 tablespoons of the mixture firmly and evenly into the bottom of each liner to form the crust.
Bake the crusts at 350°F for 5–7 minutes. Remove the pan from the oven and reduce the oven temperature to 325°F. Let the crusts cool slightly while you make the filling.
Make the filling: in a large bowl, beat 16 ounces softened cream cheese until smooth and free of lumps, scraping down the sides of the bowl as needed.
Add 3/4 cup granulated sugar to the cream cheese and beat until combined.
Add 3 tablespoons sour cream (at room temperature) and 1 1/4 teaspoons vanilla extract and mix until the mixture is smooth.
Add 2 large eggs (at room temperature) one at a time, mixing on low speed and stopping as soon as each egg is incorporated. Do not overmix.
Fill each prepared crust about 3/4 full with the cheesecake batter.
Bake at 325°F for 16–20 minutes, until the centers are mostly set but still have a slight jiggle.
Remove the pan from the oven and let the mini cheesecakes cool at room temperature for 30 minutes.
After cooling, transfer the pan to the refrigerator and chill the cheesecakes for at least 1 hour before serving.
Serve chilled, topped with whipped cream and/or fresh fruit if desired.