Add vanilla ice cream, cold milk, and peppermint extract to a blender.
Blend on high until smooth and creamy (1-2 minutes).
Churn candy canes in a food processor or mortar until crushed; add a small handful to the blender.
Pour into glasses and top with whipped cream and remaining crushed candy canes if desired.
Notes
For a non-ice cream version, substitute with blended frozen bananas.
Use fresh mint leaves as a garnish if candy canes are unavailable.
Experiment with milk alternatives (almond, oat, or soy) for vegan version.