Preheat the oven to 350 degrees.
In a medium bowl, combine eggs, oil, sugar, and vanilla mixing well.
Add baking powder, baking soda, cinnamon, and salt. Mix until combined.
Stir in the flour until fully incorporated in.
Fold in the carrots, pineapple, and walnuts.
Spray an 8×8 baking pan with non-stick 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.
Allow cake to cool completely.
While the cake cools, prepare the cream cheese frosting. In a small bowl, combine all frosting ingredients and using an electric hand mixer mix until smooth and creamy.
Frost cake with cream cheese frosting. Garnish with chopped walnuts if desired.