Begin by preheating your oven to 180°C (160°C fan) / gas mark 4 / 350°F. Prepare a 22 cm (9-inch) round cake tin by greasing it and lining both the base and sides with two layers of greaseproof paper.
In a large mixing bowl, combine the sifted flour, brown sugar, cinnamon, grated carrots, and roughly chopped walnuts.
In a separate jug, whisk together the eggs, olive oil, and milk until well blended.
Gradually pour the wet mixture into the bowl of dry ingredients, stirring continuously to ensure the batter is smooth and the flour is fully incorporated.
Transfer the batter into your prepared tin, and bake for 60 to 75 minutes. You’ll know it’s ready when a skewer (or the handle of a teaspoon if you don't have one) inserted into the center comes out clean.
Once baked, remove from the oven and allow the cake to cool in the tin for 10 minutes before turning it out onto a wire rack to cool completely.