Prep your pan. Line an 8-inch square baking pan with parchment, letting the edges overhang for easy lifting.
Lightly spritz with nonstick spray if you like.
Crush the candy canes. Place candy canes in a zip-top bag and crush with a rolling pin to a mix of small shards and fine bits. Set aside.
Melt the base slowly. In a medium, heavy-bottomed saucepan, add white chocolate chips, sweetened condensed milk, and butter. Set over the lowest heat and stir constantly with a rubber spatula until mostly melted and smooth.
Remove from heat when a few small lumps remain; they’ll melt off-heat.
Flavor it. Stir in peppermint extract, vanilla (if using), and a pinch of salt. Taste and adjust peppermint carefully—white chocolate is delicate, and a little extract goes a long way.
Fold in some crunch. Gently fold in about half of the crushed peppermint candies. This distributes pops of mint throughout the fudge.
Pour and smooth. Scrape the mixture into the prepared pan and smooth the top with an offset spatula or the back of a spoon.
Add the topping. Sprinkle the remaining crushed peppermint evenly over the surface.
Press lightly so the pieces adhere but don’t sink.
Chill to set. Refrigerate for 2 to 3 hours, or until firm enough to cut cleanly. For neat squares, wipe your knife between cuts.
Optional finish. Drizzle with melted white or dark chocolate for a bakery-style look. Let set before serving.
Serve and store. Lift the fudge out using the parchment, cut into 1-inch squares, and keep chilled or at cool room temperature.