Preheat the oven to 350°F. Lightly grease a 12-cup muffin pan.
Use an electric hand mixer to beat the butter at medium speed until creamy. Gradually add the brown sugar, beating until light and fluffy. Add the eggs, one at a time, beating just until blended after each addition.
In a medium bowl, stir together the mashed bananas, buttermilk, and vanilla. In a separate bowl, whisk together the flour, baking powder, baking soda and salt; add to the butter mixture alternately with the banana mixture, beginning and ending with the flour mixture. Beat at a low speed just until blended after each addition (do not overbeat). Spoon the batter into the prepared muffin cups, filling two-thirds full.
Bake 20 to 25 minutes, or until a toothpick inserted into the center comes out clean. Remove the muffins from the pans immediately, and cool for 10 minutes on the wire racks.