Preheat your oven to 325°F and line two large baking trays with parchment paper.

Combine chocolate and butter in a heatproof bowl set over a saucepan of simmering water and stir until melted and smooth. Set aside to cool.

Place the eggs, salt and vanilla extract in the bowl of an electric stand mixer fitted with the paddle attachment and beat on medium speed for 30 seconds. Gradually add both sugar combined, bit by bit while mixing and then increase to high speed and beat until pale and thick, about 5 minutes. You can also use an electric hand mixer, but you may need to beat for a minute longer. The mixture should fall back onto itself in ribbons when lifted with the beater. Gradually mix in cooled chocolate mixture on low speed. Mix in peppermint extract.

Stir together flour and baking powder in a small bowl. Hold a sieve over the egg mixture in the bowl and sift through the flour mixture. Fold it in gently until well combined. The batter will be quite runny, like cake batter. Refrigerate for 30 minutes to allow it to firm up slightly, but still remain spoonable. Spoon about 2 teaspoons of the mixture onto baking trays spacing them about 2 inches apart and then roll them into smooth balls. Flatten into small discs and bake for 7-9 minutes, slightly puffed, shiny and cracked at the surface. They should feel dry but still a bit soft in the center. Transfer trays to a wire rack and let cookies cool completely on trays (they are very delicate when warm and will stick to the baking tray and fall apart if removed too early). Dust with icing sugar and serve.