With an electric mixer, beat the butter, powdered sugar, vanilla extract, and peppermint extract in a large mixing bowl until light and fluffy. Beat in the flour and salt, then the nuts until evenly blended. Divide the dough in half, form each half into a disk, then wrap tightly in plastic and refrigerate for 30 minutes.

Preheat your oven to 325 degrees F and line a baking sheet with parchment paper or a silpat mat. With a cookie scoop or spoon, portion the dough and roll into 1-inch balls. Place the balls 1 inch apart on the prepared baking sheet. Bake for 15-20 minutes, until the cookies are just set but not yet brown. Transfer to a wire rack and let cool completely (if you would like to roll some of the cookies in powdered sugar to make a traditional version of snowball cookies without the chocolate and peppermint, do so now while the cookies are still warm. Leave any cookies you'd like to top with chocolate plain and let cool.)

In a heatproof bowl set over a pan of simmering water, melt the white chocolate. Ensure the bottom of the bowl does not touch the water and that the water doesn't bowl. Alternatively, you can melt the chocolate in the microwave in 15-second bursts, stirring between each and watching carefully so that the chocolate doesn't burn. When the chocolate is nearly melted, remove it from the heat (or microwave) and stir until smooth.

Dip the tops of the cookies into the white chocolate, then immediately sprinkle with crushed peppermint candies while the chocolate is still wet. Transfer to a plate to let the chocolate set. Enjoy!