Preheat the oven to 340°F / 170°C. Grease and line a loaf pan or 9-inch round cake pan.
Peel and finely grate the carrots. Press lightly only if they are very juicy.
Beat eggs and sugar for 3 to 4 minutes until pale and slightly foamy.
Add milk and oil, then mix briefly.
In a separate bowl, combine flour, baking powder, baking soda, vanilla, cinnamon and salt.
Fold dry ingredients into the wet mixture just until combined.
Fold in grated carrots and chopped walnuts.
Pour batter into the prepared pan and smooth the top.
Bake for 38 to 45 minutes, until golden and a toothpick comes out clean or with a few moist crumbs.
Cool in the pan for 10 minutes, then transfer to a rack. Cool before slicing.
Dust lightly with powdered sugar before serving, if desired.