Preheat oven to 350 degrees F (175 degrees C). Grease 3 small loaf pans.
Mix flour, baking soda, and salt together in a bowl.
Beat butter and sugar with an electric mixer in a large bowl until light and fluffy. The mixture should be noticeably lighter in color. Add 1 egg and allow to blend into the butter mixture before adding the second egg along with vanilla extract. Beat mashed bananas thoroughly into the mixture. Add flour mixture in small increments while beating until just combined into a thick batter. Fold blueberries into the batter; pour into prepared loaf pans.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 30 to 35 minutes. Cool in the pans for 10 minutes before removing to cool completely on a wire rack.
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