In a medium mixing bowl, beat the softened cream cheese, granulated sugar, and vanilla extract until the mixture is smooth and creamy. It should be thick but spreadable, with no lumps.
In a separate bowl, whip the heavy cream using a stand mixer or hand mixer on high speed until stiff peaks form. The cream should be thick enough to hold its shape when you lift the beaters.
Gently fold the whipped cream into the cream cheese mixture using a rubber spatula. Do this in batches and use slow, folding motions to keep the mixture airy. You should end up with a smooth, fluffy filling.
In serving glasses or bowls, start with a layer of red velvet cake crumbles, followed by a generous spoonful of the cheesecake filling, then a sprinkle of crushed Oreos. Repeat the layers until the glasses are full, ending with a bit of filling on top.
Top each parfait with a few mini chocolate chips if using. You can also garnish with an extra Oreo half for presentation.
Cover the glasses and refrigerate for at least 2 hours before serving. This helps the layers set and lets the flavors meld together beautifully.