On rimmed baking sheet, spread hazelnuts; roast in 325F/160C oven, tossing about halfway through, until some skin flakes off when rubbed, 10 to 15 minutes. Inside clean tea towel, rub as much of the skins as possible from still-warm nuts; let cool.

In food processor, pulse nuts with 2 tbsp/30 mL of the sugar until finely ground; pulse in flour, salt and 1/3 cup/75 mL of the sugar until well mixed. Set aside.

Beat butter until fluffy; beat in eggs and vanilla. Stir in nut mixture until thoroughly incorporated. Divide dough in half and flatten into discs. One at a time between sheets of waxed or parchment paper, roll each disc to 1/8-inch/3 mm thickness. With 2-inch/5 cm round cookie cutters, and rerolling scraps, cut out.

With spatula, transfer, about 1 inch/2.5 cm apart, to parchment paper–lined rimless baking sheets; sprinkle half of the cookies with pinch of remaining sugar. Bake in 325F/160C convection or conventional oven, rotating and switching pans, until edges are golden, about 10 or 13 to 15 minutes, respectively. Let cool in pans on racks until almost firm; transfer to racks and let cool completely.

In heatproof bowl over hot (not boiling) water, melt together semisweet and milk chocolates, stirring to blend. Spoon generous 1/2 tsp/2 mL chocolate mixture on bottom of each nonsugared cookie; top with sugared cookie, sugar side up. Let stand in cool place until chocolate mixture sets. (Make-ahead: Store in airtight container for up to 1 week.)

Makes 40 to 46 cookies.