In a small bowl, sprinkle gelatin over water. Let sit until the gelatin has bloomed, about 5 minutes.
In a small saucepan, place milk over medium low heat until it is heated through and starts to steam. Pour in the gelatin and stir until dissolved.
Place the white chocolate in a large heat-safe bowl. Pour in the heated milk and gelatin, then whisk continuously until melted and smooth. Stir in the peppermint extract.
In the bowl of a stand mixer with a whisk attachment or a bowl with a hand mixer, whisk the heavy cream until soft peaks form.
Gently fold in 1/3rd of the cream into the milk and white chocolate. Continue to fold in the remaining whipped cream until incorporated and no streaks remain.
Divide the prepared mousse among the glasses over the cookie crust. Cover and refrigerate until set, 2 hours to overnight.
Serve chilled and topped with whipped cream, sprinkles, and/or crushed candy canes.