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