Preheat the oven to 350F (180C). Line the bottom of a 6-inch (15-cm) round cake pan with baking paper, then lightly grease the sides of the pan.
In a medium bowl, whisk together the flour, cinnamon, ginger, nutmeg, baking soda and salt. Set aside.
In a separate bowl, whisk together the oil, brown sugar, egg, vanilla extract and milk until evenly combined. You should no longer see pieces of egg.
Stir the grated carrot into the oil mixture.
Make a well shape in the middle of the dry ingredients, then pour the wet ingredients into the well. Stir together until you no longer see lumps or streaks of dry ingredients.
Fold the chopped walnuts into the batter.
Pour the batter into the prepared pan. Bake in the middle of the preheated oven for about 25-30 minutes, or until an inserted toothpick comes out clean or with a few moist cake crumbs. The top should feel slightly firm to the touch.
Cool the cake in the pan for at least 15 minutes, before carefully inserting and letting the cake gently slide out.