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Preheat oven to 350F/175C degrees. 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. Set aside.
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In a mixer bowl fitted with the paddle attachment, beat eggs, brown sugar, and vanilla on high speed until light and fluffy, about 3 minutes. On a low speed, beat in melted chocolate. Mix in flour mixture just until combined. Don’t overbeat. Fold in peanut butter chips.
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Drop heaping tablespoons of dough 2 to 3 inches apart onto baking sheets. Bake until cookies are shiny and crackly yet soft in centers, 9 to 12 minutes. Cool on baking sheets for 10 minutes. Transfer to a wire rack to cool completely.
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Store cookies in an airtight container at room temperature for up to 3 days.
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Cookies can be frozen for up to 2 months. Thaw them on the counter, still covered, or overnight in the fridge.