Preheat the oven to 170 degrees Celsius (fan-assisted) and prepare a loaf tin by greasing and lightly flouring it.
In a large bowl, whisk together sugar, sunflower oil, and eggs. Then add the grated lemon zest and vanilla extract, and stir well.
In a separate bowl, mix flour, baking powder, grated carrots, chopped walnuts, cinnamon, and salt.
Gradually stir the dry ingredients into the wet ingredients until you have a smooth batter.
Pour the batter into the prepared loaf tin and smooth the surface with a spatula.
Bake the cake in the preheated oven for 40-45 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the tin before turning it out and slicing.
Enjoy your delicious walnut-carrot cake!