This cake is beloved throughout France and long ago won the heart of Julia Child, who called her version "Le Glorieux" (the glorious one). The original dessert wasn't entirely flourless: When McCall's magazine published a recipe by French cookbook writer Countess Mapie de Toulouse-Lautrec in 1959, the cake's dense texture led some to mistakenly call it "flourless," despite a small amount of flour. As the recipe evolved, flour was eventually left out completely.
Preheat the oven to 350 degrees F. Butter the bottom and sides of a 9-inch springform pan (preferably light metal); dust with cocoa powder and tap out the excess. Combine the butter and chocolate in a medium heatproof bowl set over a pan of simmering water (do not let the bowl touch the water); stir until melted and smooth. Remove the bowl from the pan and let cool to room temperature.
Meanwhile, beat the eggs, granulated sugar and salt in a large bowl with a mixer on medium-high speed until thickened and very airy, 4 to 6 minutes. Beat in the orange liqueur and vanilla. Gently fold in the melted chocolate mixture with a rubber spatula in three additions until just combined (do not overmix).
Pour the batter into the prepared pan and bake until the edges are set and the center puffs but is slightly jiggly, 30 to 40 minutes. (The cake will continue to set as it cools.) Transfer to a rack and let cool completely (the center may sink a bit). Remove the springform ring. Dust the cake with cocoa powder and confectioners' sugar just before serving.