Place the Oreo cookies in a plastic bag and gently crush them into small chunks with a rolling pin or your hands.
Add the crushed Oreos, milk, ice cubes, and sugar (if using) into the blender.
Secure the lid tightly and blend on high speed until the mixture is smooth and icy, about 30-40 seconds. You should see a thick, creamy texture with bits of cookie incorporated.
Stop the blender and check the consistency—if it's too thick, add a splash of milk and blend again for a few seconds.
Pour the slushie mixture into glasses, scooping or pouring carefully to display the cookie bits and icy texture.
Serve immediately with a straw or spoon, enjoying the thick, cold, and crunchy texture of the Oreo slushie.