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Preheat the oven to 350 F. Grease two 9-inch round pans or a 9 by 13 pan. Line with parchment if you want easy release.
In a bowl, whisk together flour, baking powder, baking soda, cinnamon, and salt.
In another bowl, whisk eggs and sugar until smooth, then whisk in oil and vanilla.
Stir the dry ingredients into the wet ingredients just until no dry flour remains.
Fold in the grated carrots, crushed pineapple (if using), and nuts (if using).
Pour the batter into the prepared pans and bake until a toothpick comes out with a few moist crumbs. For round pans, bake for 28 to 35 minutes. For the 9 by 13 pan, bake for 35 to 45 minutes.
Let the cakes cool in the pan for about 10 minutes, then turn out onto a wire rack to cool completely before frosting.
To make the cream cheese frosting, beat cream cheese and butter together until smooth.
Add vanilla and salt, then slowly add powdered sugar and taste as you go. Chill for 15 to 20 minutes if it becomes too soft.
Frost the cooled cake layers with the frosting, applying a crumb coat first if desired.