In a medium saucepan, combine the coconut milk, peppermint syrup, vanilla extract, and optional peppermint extract. Heat over medium heat until warm, stirring occasionally.
In a small bowl, dissolve the cornstarch in 2 tablespoons of cold water to create a slurry. Once the mixture in the saucepan is warm, slowly add the slurry while whisking to combine.
Continue to cook the mixture on medium heat, stirring constantly until it thickens slightly, about 3-5 minutes.
Remove the saucepan from the heat and let the mixture cool for a few minutes. Once slightly cool, stir in the crushed candy canes.
Pour the mixture into small shot glasses, filling them about three-quarters full.
Chill in the refrigerator for at least 1 hour or until set.
Before serving, top each shot with a dollop of whipped cream and sprinkle with extra crushed candy canes for garnish.
Notes
For a stronger mint flavor, add the optional peppermint extract.