Place 24 Oreo cookies into a food processor and pulse until they become fine crumbs. Reserve about 2 tablespoons of crumbs for garnishing later. Transfer the remaining crumbs to a small bowl and stir in the melted butter until the mixture looks like wet sand. Press about one tablespoon of the mixture into the bottom of 24 mini muffin liners.
In a large mixing bowl, beat the softened cream cheese and powdered sugar together until the mixture is completely smooth and free of lumps. It is important that the cream cheese is truly at room temperature to ensure a velvety texture.
Add the pumpkin puree, pumpkin pie spice, and vanilla extract to the cream cheese mixture. Continue to beat on medium speed until the color is uniform and the spices are well-distributed throughout the filling.
Gently fold in the whipped topping using a rubber spatula. Do not use a mixer for this step, as you want to keep the air in the whipped topping to ensure the cheesecake bites stay light and fluffy. Mix until no white streaks remain.
Spoon or pipe the pumpkin cheesecake mixture into the prepared mini muffin liners, filling them to the top. Smooth the tops with a small spatula or the back of a spoon for a clean finish.
Place the muffin tin in the refrigerator and chill for at least 4 hours, or ideally overnight. This allows the filling to firm up so the liners can be easily removed. Just before serving, sprinkle the reserved Oreo crumbs on top for a beautiful decorative finish.