Heat oven to 400°F. Bake pie crust as directed on package for One-Crust Baked Pie Shell. Cool completely, about 30 minutes.
Meanwhile, in 2-quart saucepan, stir together 1 1/4 cups milk and pudding mix; cook over medium heat as directed on box. Reduce heat to low; continue cooking while adding chocolate chips, stirring until melted. Set aside.
In 3-quart saucepan, heat 1/2 cup milk and marshmallows over low heat, stirring constantly, just until marshmallows are melted. Refrigerate about 30 minutes, stirring occasionally, until mixture mounds slightly when dropped from a spoon.
In chilled medium bowl, beat whipping cream and peppermint extract on high speed until stiff. Gently stir in marshmallow mixture. Gently stir in 1/4 cup of the crushed candies.
Spread chocolate mixture in cooled shell; top with whipped cream mixture. Refrigerate until set, about 4 hours. Just before serving, sprinkle remaining 2 tablespoons crushed candies on top. Store covered in refrigerator.