Preheat the oven to 350°F. Lightly spray a 9x5-inch loaf pan with nonstick spray.
In a large bowl, whisk together the flour, baking soda and salt; set aside.
In a separate bowl, use an electric mixer to combine the butter and brown sugar. Mix in the eggs and then the mashed bananas and vanilla until well blended.
Add the flour mixture and mix just until combined.
Pour the batter into the prepared loaf pan. Bake 60 minutes, or until a toothpick inserted into the center of the loaf comes out clean.
Allow the bread to cool in the pan for 10 minutes, then turn out onto a wire rack to cool completely.
Notes
This is a banana bread recipe that is full of banana flavor. Don't skimp on the bananas though- you really do need 2⅓ cups or it won't be any more special than an average banana bread.