Preheat oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
Mix dry ingredients: In a bowl, whisk together flour, baking soda, salt, and cinnamon.
Combine wet ingredients: In a separate bowl, beat eggs, sugar, oil, and vanilla extract.
Add carrots and pineapple: Stir in grated carrots and pineapple into the wet ingredients.
Combine wet and dry ingredients: Add the dry ingredients into the wet mixture and stir until just combined.
Pour and bake: Divide the batter evenly between the pans and bake for 30-35 minutes.
Cool: Allow cakes to cool in the pans for 10 minutes, then transfer to a wire rack to cool completely.
Make frosting: Beat together cream cheese, butter, powdered sugar, and vanilla until smooth.
Frost cake: Once cooled, spread frosting on top of the first layer, place the second layer on top, and frost the entire cake.