Preheat oven to 200 degrees. In a food processor, pulse to combine chestnut flour, walnuts, 1/3 cup sugar, and the cinnamon until nuts are ground to a fine powder. Transfer to a large bowl.

Whisk egg whites and salt with an electric mixer on high speed until soft peaks form. Continue to whisk, gradually adding remaining 2/3 cup sugar in a slow stream, until whites are very stiff and glossy, 11 to 13 minutes. Gently fold egg whites into chestnut-flour mixture with a flexible spatula just until combined.

Transfer one-third of mixture to a pastry bag fitted with a 1/4-inch plain tip, and pipe 1-inch circles, 1 1/2 inches apart, on parchment-lined baking sheets, holding pastry bag vertically, then pulling up to create a peak. Bake until completely dry and crisp, about 2 hours. Let meringues cool completely on sheets on a wire rack.

Temper chocolate: Melt chocolate in a small bowl set over (not in) a saucepan of barely simmering water. Using a chocolate or candy thermometer, melt until temperature registers 115 degrees. Remove bowl, wiping away moisture from bottom of bowl. Leave water at a simmer. Stir chocolate, cooling it until temperature reads 83 to 85 degrees. Replace bowl over simmering water in 30-second intervals until thermometer reaches 88 to 89 degrees. Transfer to another bowl to cool. Use immediately.

Holding a cookie by one side, dip in tempered chocolate until half is submerged. Gently shake off excess chocolate. Place dipped meringues on a parchment-lined baking sheet and let set completely without disturbing. Meringues can be stored in an airtight container at room temperature up to 5 days.