Step 1Heat oven to 350 degrees. Line two large cookie sheets with parchment paper.
Step 2Smash and mix the butter into the brown sugar with a wooden spoon in a bowl until the butter is no longer visible and the sugar resembles wet sand. Add the peanut butter, vanilla and egg and mix until well combined. Lift the spoon out of the dough. If the dough drips off in globs, refrigerate or freeze it until stiff. Cold dough will bake into taller cookies too.
Step 3Drop rounded teaspoons of dough onto the prepared sheets, spacing 1 ½ inches apart. Sprinkle the tops with salt and then with peanuts.
Step 4Bake one sheet at a time until darker brown around the edges and dry on top, 9 to 11 minutes. Cool completely on the sheets on a rack.
Vegan peanut butter cookies
Mix 1 tablespoon ground flax seeds with 1 tablespoon cold water. Let stand until thickened, about 5 minutes. Substitute coconut oil for the butter and the flax mixture for the egg. Proceed as above.
PB&J sandwich cookies
Spread a thin layer of thick jam on half the cookies and sandwich with the others.
Peanut butter and salted caramel ice cream sandwiches
Sandwich small scoops of salted caramel ice cream between cookies and freeze until firm.