Place 48 small candy cups on a sheet pan.
Bring cream to a simmer in a medium saucepan. Remove from heat. Whisk in 1 pound white chocolate, until melted and smooth.
Mix in crushed peppermint candies and peppermint extract. Fill a pastry bag or use a small spoon to fill candy cups about ⅔ full.
Using a wet finger, smooth down the top of each peppermint cream. Refrigerate until set, about 15 minutes.
While the peppermint creams are setting, melt 12 ounces semi-sweet chocolate in a double boiler or in a bowl set over a pan of boiling water. Stir until smooth.
Top each peppermint cream with ½ teaspoon of melted chocolate.
Sprinkle each cup with remaining candy cane dust.
Chill candies until set, about 1 hour.
Store in an airtight container in the refrigerator. Peppermint creams will stay fresh for about 2 weeks.
