Prepare a 7” springform pan with nonstick spray and set aside.
In a large bowl using a hand mixer (you can also use a stand mixer with a paddle attachment) combine the vegetable oil, brown sugar, and granulated sugar and mix until combined and fluffy.
Add in eggs and vanilla and mix until combined.
Sift in Flour, baking soda, cinnamon, nutmeg, and salt and fold into the wet ingredients until well combined. Add in the carrots and fold to distribute evenly.
Pour the carrot cake mixture into the bottom of the springform pan.
In another large bowl, add the cream cheese and cream on a high speed for 3-4 minutes or until there are no lumps. Make sure to scrape down the sides of the bowl 2-3 times during this process.
Add in the sugar and flour and mix well until combined and fluffy. Scrape the sides and bottom of the bowl.
Add in the sour cream and vanilla extract and mix until just combined. Scrape the sides and bottom of bowl.
Make sure there are no lumps in the batter. If there is, mix for an additional few minutes and scrape down the sides and bottom of the bowl.
Add the eggs one at a time, making sure to completely combine the first before adding the second. Be careful not to overmix here, you just want to mix long enough that you don’t see the yolk anymore.
Place the cheesecake filling on top of the carrot cake and gently tap on the counter to remove any air bubbles.
Cover the spring form pan completely with aluminum foil making sure to seal well around the top.
Using another piece of aluminum foil, make a sling by folding the foil from long end to long end. Place underneath the cheesecake to help you drop it down into the Instant Pot.
Prepare your Instant Pot by adding in the trivet and adding one cup of water.
Place the cheesecake on the trivet and seal the lid.
Set your pot on high pressure for 45 minutes and allow to naturally release.
Once you can open the lid, remove the cheesecake and allow to cool on the counter. Once cooled, place in the refrigerator for at least four hours but best overnight.
Once you are ready to serve, combine the cream cheese and butter in a medium size bowl and mix until light and fluffy. Add confectioners’ sugar and vanilla and mix well for 4-5 minutes. Add the frosting to the top of the cheesecake and drizzle with caramel and top with walnuts or pecans. Enjoy!