Place the chocolate ice cream or milk into the blender, creating a smooth base for the slushie.
Add the crushed ice to the blender, then secure the lid tightly.
Blend the mixture on high speed until the ice is broken down and the mixture becomes thick and slushy, about 30-45 seconds. You should see the texture turn creamy with icy bits dispersed evenly.
Add the chopped chocolate bits into the blender and pulse a few times just to incorporate them evenly without crushing them completely, so they remain crunchy.
Pour the thickened, chocolatey slushie into chilled glasses, filling them nearly to the top.
Serve immediately with a straw or spoon, enjoying the crunchy bits and velvety ice. Feel free to garnish with extra chocolate shavings if desired.