Preheat oven to 350°F (175°C) and grease a cake pan or line it with parchment paper.
In a large bowl, whisk the eggs and sugar until light and fluffy.
Add the milk and oil, mixing until fully combined.
Sift in the flour, baking powder, vanilla, and cinnamon. Gently fold the ingredients together, being careful not to overmix.
Stir in the grated carrots and chopped walnuts, ensuring they are evenly distributed.
Pour the batter into the prepared cake pan and smooth the top.
Bake for 40-45 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool completely before slicing. Serve as is, or top with a dusting of powdered sugar or a simple glaze.