Place 7 oz. (a little more than half) of the chocolate and the butter into a small saucepan over medium-low heat. Stir until everything is melted and smooth. Set aside.
Meanwhile, in the bowl of a stand mixer, mix the eggs, sugar, and vanilla (using a paddle attachment) until the mixture is pale yellow, fluffy, and smooth.
Add the flour, baking powder, and melted chocolate to the egg mixture and mix well. Add the remaining unmelted chocolate bits and mix just until everything is combined. Allow batter to stand for 10 minutes.
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