Preheat your oven to 325°F (165°C). Grease two 8×4-inch loaf pans extremely well and dust lightly with flour to promote doneness without sticking.
Combine egg in a large mixing bowl and whisk to a light yellow frothy texture. Add the white sugar, mashed bananas, grated zucchini, vegetable oil, brown sugar, and vanilla extract gradually. Once all the ingredients are incorporated and the batter is smooth, mix.
In another bowl, whisk together the flour, ground cinnamon, baking powder, baking soda and salt. Gradually add dry ingredients into the wet mixture, stirring until just incorporated. Carefully fold in the dried cranberries and chopped walnuts, mixing to combine throughout the batter.
Spoon the batter evenly into the two prepared loaf pans. Fill the pans and bake in the oven until a toothpick inserted into the center comes out clean, 45 to 50 minutes.
The loaves should cool in the pans on a wire rack once baked. Let cool completely and then remove the bread from the pans, slice and serve.