Whisk together thoroughly:
1 1/3 cup flour
¾ teaspoon salt
½ teaspoon baking soda
¼ teaspoon baking powder

In a large bowl, beat on high speed until lightened in color and texture, 2 to 3 minutes:
5 1/3 tablespoons unsalted butter (room temperature)
2/3 cup sugar

Beat in the flour mixture until blended and the consistency of brown sugar. Gradually beat in:
2 large eggs slightly beaten (room temperature)

Fold in just until combined:
3 very ripe bananas
½ cup coarsely chopped nuts

Preheat oven to 350F

Bake for 50 to 60 minutes.