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Heat oven to 375 degrees (F).
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Using an electric mixer set on high speed, cream the butter and sugars in a large bowl.
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Lower to medium speed and add the egg, peanut butter, and vanilla.
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Sift together the flour, baking soda, and salt.
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Add to the butter mixture on low speed.
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Beat until incorporated.
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Fold in the rice cereal and peanuts.
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Form the dough into approximately 1 1/2-inch balls.
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Place on parchment-or foil-lined baking sheets, 2 inches apart.
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Gently press the cookies with the back of a fork to create classic hatch marks.
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Use your thumb to create a shallow well in the center of each cookie and fill with a spoonful of jam, if desired.
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Bake until golden brown, about 12 minutes.
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Let cool on sheets for 5 minutes, then transfer to wire racks.