Preheat the 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 the heat.

Beat eggs and sugar together in a bowl with a whisk or 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 the chocolate mixture; stir to combine. Pour chocolate mixture into remaining egg mixture and stir until combined. Pour batter into the prepared pan.

Bake in the preheated oven until just barely set, with a jiggle below the surface, 14 to 15 minutes. Cool to room temperature, about 30 minutes. Wrap in aluminum foil and refrigerate until chilled, at least 1 hour.