Line a 9x13-inch pan with parchment and lightly grease the paper.
Melt the butter in a large pot over medium-low heat.
Add most of the marshmallows, saving about 1 cup. Stir until fully melted and smooth.
Remove from heat. Stir in peppermint extract, vanilla, and salt.
Fold in the cereal and finely crushed candy canes until coated. Gently mix in the reserved marshmallows.
Press the mixture into the pan with a buttered spatula, patting lightly without compacting too hard.
Microwave white chocolate in 20-second bursts, stirring between each, until smooth. Drizzle over the bars.
Sprinkle the remaining crushed candy canes on top. Let set 30 minutes, then cut into squares.