In a medium bowl, cream together the butter, brown sugar and white sugar. Beat in the egg and vanilla. Combine the flour, salt and baking soda, stir into the creamed mixture. Finally, stir in the granola, chocolate chips and peanuts. Drop dough by heaping teaspoonfuls onto greased cookie sheets, about 2 inches apart.
Bake 12 to 15 minutes in the preheated oven, until cookies are lightly browned around edges. Remove cookies to wire racks and allow to cool.