Heat the oven to 275°F (135°C). Line a standard 12-cup muffin tin with paper liners, then place one whole Oreo in the bottom of each liner.

Beat the softened cream cheese and granulated sugar on medium speed until smooth, scraping down the bowl as needed. Add the eggs one at a time, mixing just until each one is incorporated, then mix in the vanilla.

Fold the coarsely chopped Oreos into the cheesecake batter by hand. Avoid overmixing so the filling stays smooth and the cookie pieces remain distinct.

Divide the batter evenly among the prepared liners, filling each about three-quarters full. Bake for approximately 22 minutes, or until the centers look set but still have a slight jiggle.

Cool the cheesecakes in the pan, then refrigerate until completely firm. Chill for at least 1 hour before serving, with 2 to 4 hours recommended for the best texture, and finish with whipped cream or Oreo pieces if desired.