Mix together the butter, peanut butter, granulated sugar, and brown sugar until creamy.
Add eggs and vanilla and beat until light.
Sift the flour with the soda and salt; stir into creamed mixture until well blended.
Lightly mix in the shredded wheat and peanuts.
Drop rounded teaspoonfuls of batter, about 2 inches apart, on ungreased cookie sheets. (This makes rather ragged cookies, so I like to roll them into balls first, but little pieces of shredded wheat DO stab a bit!) Using the tines of a fork, press dough flat in each direction to make a crisscross pattern on top of each cookie.
Bake in a 350 degree oven for about 10 to 12 minutes or until lightly browned.