Place the Oreo cookies in a blender and pulse a few times until finely crushed, resembling sand with some larger pieces for texture.
Add the milk and sweetened condensed milk to the crushed cookies in the blender.
Drizzle in the vanilla bean paste for a fragrant boost of flavor.
Secure the lid on the blender and blend everything on high for about 30-45 seconds until the mixture is smooth and frothy, with cookie bits still visible.
Check the consistency; it should be thick, icy, and slightly granular from the crushed cookies.
Pour the slushie into glasses, using a spoon to help scoop the thick mixture if needed.
Optionally, garnish with additional crushed Oreos or a drizzle of chocolate syrup for presentation.
Serve immediately with a straw or spoon for a refreshing, icy treat.