Move oven rack to middle tier and preheat oven to 350 degrees F (175 degrees C). Line 24 mini-muffin cups with miniature paper liners.
Beat cream cheese, eggs, and sugar together in a bowl until smooth.
Put 1 cookie into the bottom of each paper liner. Spoon the cream cheese mixture atop the cookies.
Bake in preheated oven until nearly set in the middle, about 15 minutes.
Move tins to a wire rack to cool slightly before refrigerating until the cheesecake layer sets firmly, about 3 hours.
To make a holiday version, add 1/4 teaspoon peppermint extract, a few drops of red or green food coloring, and 2 or 3 crushed candy canes to the cream cheese mixture. Use candy cane Oreo(R) or peppermint wafers for the cookie base. Sprinkle finished cheesecake with more crushed candy cane or holiday sprinkles.
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