Heat oven to 350°F. Grease an 8-by-4 inch loaf pan.
In a large bowl, combine the applesauce, honey, and brown sugar. Add the eggs and beat well. Stir in the mashed bananas and almond milk. Add the baking soda, vanilla extract, cinnamon, and 1/2 teaspoon salt and stir.
Gradually fold the flour into the banana mixture until just combined (do not overmix).
Pour the batter into the prepared pan and bake until a toothpick inserted into the center of the loaf comes out clean, 45-50 minutes. Cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.
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