Preheat oven to 400*F. Grease 12 standard size muffin cups or use paper liners.
Beat together butter and sugar at medium speed until light and fluffy. Add eggs, 1 at a time, Beat in bananas until smooth.
Mix together flour, salt, baking powder, and baking soda.
Stir in nuts and vanilla. Do not over mix batter; it should not be completely smooth.
Spoon batter into prepared pan, filling 2/3 full. Bake until lightly golden, 15 to 18 minutes. Transfer muffin-pan cups to a wire rack to cool, slightly. Turn out onto rack. Serve warm.
Notes
When adding liquid to flour mixture, stir only until dry ingredients are moistened.
If you do not have sufficient batter to fill every muffin cup, fill empty cups halfway with water so the pan doesn't warp.
To test the freshness, of baking powder, mix 1 tsp of baking powder with 1/3 cup hot water; if mixture does not foam, the powder is stale and should not be used.