Preheat the oven to 350°F and spray a 9×13 inch metal baking pan with nonstick spray.
In a large bowl, whisk together the vegetable oil, granulated sugar, brown sugar, vanilla, and eggs until combined.
Add the flour, corn starch, baking soda, and salt to the wet ingredients and whisk until just combined. Fold in the shredded carrots with a rubber spatula.
Pour the batter into the prepared pan and bake for 35-40 minutes, or until a toothpick comes out clean. Let the cake cool completely.
Once melted, stir in the butter one tablespoon at a time. Slowly drizzle in the room-temperature heavy cream, about 2 tablespoons at a time, until fully combined. Be cautious as it will bubble and steam.
Remove the caramel from heat and stir in the salt. Allow it to cool to room temperature before using. Store in the refrigerator for up to 2 weeks.
#### For the Frosting:
In a stand mixer bowl, beat the butter and cream cheese on medium-high speed until smooth and combined, about 2 minutes.
Add the vanilla and powdered sugar, and mix until smooth.
#### For Assembly:
Once the cake has cooled completely, top it with cream cheese frosting.
Drizzle about 1/2 – 3/4 cup of room-temperature caramel on top. Use a spatula or spoon to swirl the caramel into the frosting.
Refrigerate until serving and store in the fridge for up to 5 days.