Preheat the oven to 350 degrees F (175 degrees C). Lightly grease an 8x4-inch loaf pan.
Sift flour, baking soda, and salt into a bowl.
Beat brown sugar and peanut butter in a large bowl until creamy. Beat in egg and vanilla until smooth. Mix in flour mixture alternately with buttermilk, beating until smooth after each addition. Spoon batter into the prepared pan.
Bake in the preheated oven until nicely browned and a toothpick inserted into the center comes out clean, about 1 hour. Remove from the pan to cool.