Make the crust: Position a rack in the lower third of the oven and preheat to 375 degrees F. Pulse the cookies and granulated sugar in a food processor until finely ground. Add the melted butter and pulse until combined.
Lightly coat a 9-inch tart pan with a removable bottom with cooking spray. Press the crumb mixture into the bottom and up the side of the pan. Bake until set, about 15 minutes, then transfer to a rack to cool completely.
Meanwhile, make the filling: Heat the milk in a saucepan over medium-high heat until it starts simmering, then remove from the heat. Whisk the egg yolks, granulated sugar, cornstarch and salt in a medium bowl until combined. Gradually whisk one-third of the warm milk into the egg mixture, then pour into the saucepan with the remaining milk. Cook over medium heat, whisking constantly, until the mixture starts to bubble and thicken, about 3 minutes. Continue boiling, whisking, until the mixture is thick like pudding, about 2 more minutes. Remove from the heat, then whisk in the semisweet and mint-flavored chocolate and the butter. Pour into the prepared crust and spread evenly. Refrigerate until set, about 1 1/2 hours.
Right before serving, beat the heavy cream, confectioners' sugar and peppermint extract in a medium bowl with a mixer on medium speed until soft peaks form. Spread the whipped cream on the tart and sprinkle with sanding sugar.