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Preheat oven to 350°F/175°C. Line tow baking sheets with parchment paper and set aside.
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Put butter and chocolate in a heat-proof bowl and microwave in 20-second increments, stirring between each, until melted. Do not overheat.
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In another bowl, whisk together flour, baking powder, and salt.
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In a mixing bowl, beat eggs, brown sugar, white sugar and vanilla on high speed until light and fluffy. Reduce speed to low; beat in melted chocolate. Mix in flour mixture until just combined.
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Drop 1 teaspoon of dough 2 to 3 inches apart onto baking sheets. Bake, rotating sheets halfway through until cookies are shiny and crackly yet soft in centers, 7 to 9 minutes.
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Cool on baking sheets 10 minutes; transfer to a wire rack to cool completely.