Preheat the oven to 350°F. Line a muffin pan with cupcake liners.
In a medium bowl, combine 1 1/2 cups graham cracker crumbs, 5 tablespoons melted unsalted butter, and 1 1/2 tablespoons granulated sugar. Stir until the crumbs are evenly moistened.
Divide the crust mixture among the liners, pressing about 1 1/2 tablespoons into the bottom of each liner and compacting it evenly. Bake the crusts for 5–7 minutes, until set. Remove the pan from the oven.
Reduce the oven temperature to 325°F.
In a large bowl, beat 16 ounces softened cream cheese with an electric mixer until smooth and lump-free.
Add 3/4 cup granulated sugar and beat until combined. Mix in 3 tablespoons sour cream and 1 1/4 teaspoons vanilla extract until smooth.
Add 2 large room-temperature eggs one at a time, mixing on low speed and scraping the bowl after each addition. Mix just until the eggs are incorporated; do not overmix.
Spoon the cheesecake batter over the baked crusts, filling each liner about 3/4 full and smoothing the tops.
Bake at 325°F for 16–20 minutes, until the edges are set and the centers have a slight jiggle.
Remove the pan from the oven and let the mini cheesecakes cool at room temperature for 30 minutes. Then refrigerate the pan and chill for at least 1 hour before serving.
Serve chilled, topped with whipped cream and/or fresh fruit if desired.