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In a large mixing bowl, cream together the butter, brown sugar, and granulated sugar on medium speed.
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While continuing to mix on medium speed, add in the egg and egg yolk.
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Turn the speed down to low and add in the flour ½ cup at a time until thoroughly mixed together.
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Fold in the baking soda, baking powder, cornstarch, salt, and Reese's Pieces with a plastic spatula.
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Cover with plastic wrap and allow to chill in the refrigerator for at least 3 hours. Overnight is best.
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Preheat oven to 350 degrees and line a baking sheet with parchment paper or a silicone baking sheet.
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Spoon the cookie dough onto the baking sheet and bake for 9-10 minutes.
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Allow to cool 1-2 minute before transferring to a cooling rack.