How to Make It
Preheat the oven to 350°. Spread the nuts on a baking sheet and toast for about 8 minutes, until light golden. Let cool.
In a medium bowl, using a hand mixer, beat the butter with both sugars at medium speed until light and fluffy, about 3 minutes. Beat in the vanilla, then add the flour and salt and mix just until a dough forms. Stir in the nuts. On a sheet of parchment paper, roll out the dough 1/4 inch thick. Transfer the parchment and dough to a baking sheet and refrigerate for 1 hour.
Line 2 baking sheets with parchment paper. Using a 11/2 -inch cookie cutter, stamp out rounds from the dough and arrange them 1 inch apart on the prepared sheets. Gather the scraps and stamp out more rounds. Refrigerate the cookies for 1 hour.
Bake the cookies for about 12 minutes, rotating the baking sheets halfway through, until golden. Transfer to a rack to cool.
In a heatproof medium bowl, combine both of the chocolates. In a small saucepan, bring the cream to a simmer. Pour the cream over the chocolate and let stand for 2 minutes; stir until smooth. Stir in the peppermint extract and salt and refrigerate for about 1 hour, until thick.
Spread 1 1/2 teaspoons of the filling on the underside of half of the cookies and sandwich with the remaining cookies.