Preheat Oven: Preheat the oven to 356°F (180°C). Line a 9 x 5-inch (23 x 13 cm) loaf tin with parchment paper. Set aside.
Mix Dry Ingredients: In a medium-sized mixing bowl, whisk together the flour, baking powder, baking soda, cinnamon, allspice, nutmeg, ginger, and salt. Set aside.
Mix Wet Ingredients: In a large mixing bowl, whisk together the oil, yogurt, eggs, brown sugar, granulated sugar, and vanilla until smooth and well combined.
Add Carrots: Mix in the shredded carrot until distributed.
Combine Mixtures: Add the dry ingredients to the wet ingredients and gently fold until just combined. Avoid overmixing.
Add Walnuts: Fold in the chopped walnuts until evenly distributed through the batter. The mixture will be thick.
Bake: Pour the batter into the prepared loaf tin and smooth the surface. Bake for 50-55 minutes, or until a skewer inserted into the center comes out clean or with a few moist crumbs.
Cool: Allow the cake to cool in the pan for 15 minutes before transferring to a wire rack to cool completely.