Preheat oven to 425 degrees F (220 degrees C). Butter and flour a 9-inch cake pan.
Melt semisweet chocolate and unsalted butter together in the top of a double boiler over simmering water, stirring frequently and scraping down the sides with a rubber spatula, until chocolate and butter are completely melted and combined. Remove from heat.
Beat eggs and sugar together in a bowl with a whisk or an electric mixer until pale and very thick, 5 to 10 minutes. Sift in flour, cayenne, and salt; whisk to combine.
Pour 1/4 of the egg mixture into chocolate mixture; stir to combine. Pour chocolate mixture into remaining egg mixture and stir until cake batter is combined. Pour batter into prepared cake pan.
Bake in the preheated oven until just barely set, with a jiggle below the surface, 14 to 15 minutes. Cool to room temperature, wrap in aluminum foil, and refrigerate until chilled, at least 1 hour.