Preheat oven to 350°F degrees. Grease and flour a 9" by 5" loaf pan.
Sift flour, baking soda, and salt together in a bowl. Set aside.
In a large bowl, cream together brown sugar and peanut butter until fluffy.
When measuring sour cream, pour liquid off the top of sour cream, and use thick sour cream on bottom of container. Add thick sour cream, egg, mashed bananas, and vanilla to the peanut butter mixture, and mix well.
Add flour mixture to peanut butter mixture, and mix just until combined while scraping bottom of bowl. Pour into prepared loaf pan.
Bake for 40 minutes. Remove from oven and cover with double layer of aluminum foil to prevent excess browning. Return to oven and bake for 20 minutes more, or until toothpick inserted in center comes out clean. Cool in pan for 10 minutes on wire rack.
Remove from pan and allow to cool completely on a wire rack. When cool, wrap in plastic wrap and aluminum foil and allow to set for 3 days at room temperature to combine flavors before cutting or consuming (Setting for 3 days makes the loaf moister and tastier). Then, refrigerate.