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Preheat oven to 325 degrees F (165 degrees C). Spray a full size bread pan with non-stick cooking spray, and lightly dust with flour.
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In a large bowl, beat eggs and sugar in a large bowl until light and fluffy, about 5 minutes.
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Beat in bananas, applesauce, milk, oil and vanilla.
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In a separate bowl, sift together flour, baking powder, baking soda and salt.
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Stir flour mixture into banana mixture, mixing just until blended.
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Fold in walnuts.
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Pour batter into prepared pan do not fill more than 1/2 full - if you are using smaller pans, be sure not to fill them more than 1/2 full or they will overflow while baking.
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Bake in preheated pan until golden and a toothpick inserted into center of the loaf comes out clean, about 1 hour.
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Turn bread out onto a wire rack and let cool.