Preheat the oven to 400 degrees F (200 degrees C). Grease and flour four 6-ounce ramekins.
Place chocolate and butter in the top of a double boiler over simmering water. Stir frequently, scraping down the sides with a rubber spatula to avoid scorching, until chocolate is melted, about 5 minutes.
Combine eggs and sugar in a large bowl; beat with an electric mixer until pale and thick, about 5 minutes. Mix in melted chocolate, cocoa powder, and flour until combined. Pour batter into the prepared ramekins and place on a baking tray.
Bake in the preheated oven until the sides are set but the middle is still jiggly, 10 to 13 minutes. Let cool for 5 minutes before serving.
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