Prepare the crust: Place 18 Oreos in a food processor and pulse until finely crushed. (No food processor? Place cookies in a sealed zip-top bag and crush with a rolling pin.) Transfer crumbs to a bowl and mix thoroughly with melted butter until the mixture resembles wet sand.
Form the base: Divide the Oreo mixture evenly among 6 glasses or dessert cups, pressing firmly with the back of a spoon to create a compact base. Set aside while preparing the filling.
Make the cheesecake filling: In a large mixing bowl, beat the softened cream cheese, granulated sugar, and vanilla extract with an electric mixer on medium speed until completely smooth and no lumps remain, about 2-3 minutes. Stop to scrape down the sides of the bowl as needed.
Whip the cream: In a separate bowl, whip the heavy cream and powdered sugar until stiff peaks form. The cream should hold its shape when you lift the beaters.
Combine the mixtures: Gently fold the whipped cream into the cream cheese mixture using a rubber spatula, maintaining as much air as possible for a light, fluffy texture. Continue folding until just combined with no white streaks.
Add Oreo pieces: Crush the remaining 6 Oreos into chunky pieces and gently fold about two-thirds of them into the cheesecake mixture, reserving the rest for topping.
Assemble the cups: Spoon or pipe the cheesecake mixture over the Oreo crusts, dividing equally among the glasses. Smooth the tops with the back of a spoon.
Garnish and chill: Sprinkle the reserved Oreo pieces over the tops of each cup. Cover with plastic wrap and refrigerate for at least 2 hours or overnight until set and thoroughly chilled.