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In a blender or food processor, add the sugar and chocolate pieces and pulse to process until the chocolate is very finely chopped.
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In the microwave or on the stove, heat the whole milk until just bubbling around the edges.
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Add the hot milk to the chocolate and sugar in the blender and process until smooth.
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Pour chocolate mixture into a medium-sized bowl and let cool completely.
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Stir in the heavy cream and vanilla and chill for 30 minutes or longer.
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Add to your ice cream maker and follow the manufacturer's instructions. Then transfer to an airtight container. While transferring, drop little balls of peanut butter cookie dough in the ice cream.
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Cover and freeze for several hours or overnight.