In a small bowl, combine the eggs, oil, sugar and vanilla. Mix well.
Add the baking powder, baking soda, cinnamon and salt. Mix until combined.
Mix in the flour, stirring until the flour is fully incorporated in.
Fold in the carrots and walnuts.
Spray an 8x8 baking pan with cooking spray. Spread the batter in the prepared pan.
Bake at 350 degrees for 35-37 minutes, until a toothpick inserted in the center comes out clean.
Once the cake has cooled, sprinkle powdered sugar on top and serve.
The calories shown are based on the cake being cut into 9 pieces, with 1 serving being 1 slice of cake. Since different brands of ingredients have different nutritional information, the calories shown are just an estimate. **We are not dietitians and recommend you seek a nutritionist for exact nutritional information. The information in the nutrition box are calculated through a program and there is room for error. If you need an accurate count, I recommend running the ingredients through your favorite nutrition calculator.**