In a small saucepan melt the butter until it turns brown and smells nutty. It will foam up and turn brown around 5 minutes so make sure to keep an eye on it. Remove from heat immediately and add the white and brown sugars. Let sit for about 5 minutes to cool. Pour into a large mixing bowl and add the egg and vanilla. Mix in banana and sour cream.
In separate bowl, combine flour, baking soda, baking powder and salt. Fold into banana mixture.
Fold in the chocolate chips and nuts. Dough will be wet.
Refrigerate dough for at least 30 minutes. Drop a one inch ball of dough onto cookie sheets 2-inches apart and bake at 350 degrees for 10-12 minutes or until edges are brown. Do not overbake these! Cookies will get more moist as they sit.