In a large bowl, combine brown sugar, white sugar, and oil until no lumps remain. You can use a stand mixer or a hand mixer. Add eggs and vanilla and blend until combined.
Sift in flour, cinnamon, baking soda, nutmeg, and cloves. Stir to combine. The batter will be very thick, like soft peanut butter or loose cookie dough.
Add carrots, nuts, pineapple, and coconut. Stir well, then let rest for 5-10 minutes to allow the moisture from the carrots and pineapple to soften the batter. Stir once more.
Evenly divide the mixture between two greased, six inch cake pans. Cover tightly with foil.
To the Instant Pot, add 2 cups of water. Place one cake pan onto a silicone pressure cooking sling or trivet and place it in the Instant Pot. Place a trivet (or other oven/pressure cooking safe rack) on top of the first cake pan. I used the rack from my air fryer, but anything that will allow adequate airflow between the cake pans will work. Try two chopsticks, or the trivet. Place the second cake pan on top.
Lock the lid, turn the knob to sealing, and cook on manual high pressure for 60 minutes. Allow a full natural pressure release, about 15-30 minutes.
Carefully remove cakes from the pot, remove the foil, and let cool to room temperature. Replace with foil or cover with plastic wrap, then refrigerate for at least 5 hours, overnight preferred.
Remove the cakes from the pans. The cakes will shrink a little bit and might stick. I recommend sliding a knife around the edges of the pan, then shaking the pan from side to side (with the foil back on it) to dislodge the cake. It should then pop out perfectly.
Ice the cake with cream cheese frosting and decorate with additional chopped nuts, coconut, frosting, and pineapple. I recommend crumb coating the cake by adding a thin layer of frosting to the entire cake, then freezing for 15-20 minutes. Then, frost with the remaining frosting. This will help lock in the crumbs and yield a beautiful cake!