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Coarsely chop the unsweetened chocolate.
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Melt the butter and chocolate in a saucepan over low heat. Stir and melt until smooth.
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Beat the eggs and sugar at medium speed with a stand mixer or a hand mixer. Beat until the mixture is well blended.
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Once the chocolate is melted, turn the mixer down to low and slowly drizzle the chocolate into the mixture. Continue to blend until the chocolate is fully mixed in.
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With the mixer still on low, gradually add the flour and vanilla until fully incorporated.