Preheat the oven to 320°F (160°C). Grease and line an 8-inch (20 cm) round cake pan with parchment paper.
In a heatproof bowl, combine the chopped dark chocolate and unsalted butter. Melt over a double boiler or in short bursts in the microwave, stirring until smooth. Set aside to cool slightly.
In a separate bowl, whisk the egg yolks with half of the granulated sugar (35 grams) until the mixture becomes pale and slightly thickened.
Add the melted chocolate and butter mixture to the egg yolk mixture. Stir gently to combine.
Sift the cake flour, cocoa powder, and salt together. Gradually fold the dry ingredients into the chocolate mixture until just combined.
Add the milk and vanilla extract to the batter and gently mix until smooth.
In a clean bowl, beat the egg whites with cream of tartar until foamy. Gradually add the remaining granulated sugar (35 grams) while continuing to beat until stiff peaks form.
Gently fold one-third of the beaten egg whites into the chocolate batter to lighten it. Then carefully fold in the remaining egg whites in two additions, being careful not to deflate the mixture.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake in the preheated oven for 20 to 25 minutes, or until a toothpick inserted into the center comes out with moist crumbs but no wet batter.
Remove the cake from the oven and let it cool in the pan for 10 minutes. Then transfer to a wire rack to cool completely before serving.