Preheat the oven to 400°F (200°C) and grease a loaf pan, lining it with parchment paper.

In a large mixing bowl, combine the egg, brown sugar, granulated sugar, vegetable oil, vanilla extract, and yogurt. Whisk until smooth.

In a medium bowl, sift together the all-purpose flour, baking soda, baking powder, and salt. Gradually fold the dry ingredients into the wet mixture.

Gently fold in the shredded carrots and zucchini, along with crushed walnuts if using. Avoid overmixing.

Pour the batter into the prepared loaf pan and bake for approximately 1 hour, or until a toothpick comes out clean.

Let the loaf cool in the pan for 10-15 minutes before transferring it to a wire rack to cool completely.

Optionally, drizzle with vanilla or caramel icing once the loaf has cooled.