Preheat oven to 350 degrees F and line an 8-inch square baking pan with parchment paper on all sides by laying one piece of paper one way and then another piece of the opposite way.

In a large bowl, stir oil and sugar together with a wooden spoon (do not use a mixer). Add eggs, vanilla, pineapple, and carrots. 

In a separate bowl, stir together flour, baking powder, baking soda, cinnamon, and sea alt. 

Sprinkle the dry ingredients over the wet and stir until combined. 

Pour batter into prepared baking pan and bake 33 - 36 minutes until the cake is a nice golden brown, starting to pull away from the edges of the pan, and a toothpick inserted in the middle comes out with just a few crumbs attached. 

Cool cake in pan for 20 minutes, use parchment to carefully lift cake out, and then cool completely on a wire rack. 

As cake cools, make frosting. First, melt the caramel bits in the microwave with a splash of water, or make homemade caramel and set aside to cool slightly.

With an electric mixer, beat cream cheese and powdered sugar until light and fluffy. Stir in caramel, vanilla, and sea salt. 

Frosting cake with caramel cream cheese frosting and serve.