Preheat the oven to 375 degrees F. Coat 2 (4 1/2 by 8 1/2-inch) loaf pans with nonstick spray. Line the pans with parchment paper and spray the paper.
Combine the zucchini, apple, brown sugar, oil, eggs and vanilla extract in a large bowl and stir to combine. Add 3 cups flour, salt, baking powder, baking soda, cinnamon and nutmeg to the bowl and mix well. Toss the nuts with the remaining1/2 teaspoon flour to coat and prevent them from sinking. Gently stir in the nuts and the extract.
Divide the batter between the 2 loaf pans. Bake until a toothpick or skewer inserted in the middle of each loaf comes out clean, 50 minutes to 1 hour. Remove the bread from the pans and cool on a wire rack.