Preheat the oven to 350 Degrees F and grease a 7" or 8" Springform pan with non-stick spray.
In a large bowl, beat together the erythritol and butter until fluffy. Beat the eggs in, then the almond milk and vanilla. Next, beat in the almond flour, coconut flour, baking powder, and spices.
Fold in the shredded carrot and mix just until it is well integrated into the batter.
Transfer to prepared pan and bake for 20-25 minutes or until a toothpick inserted into the center of the cake comes out clean.
Allow to cool to the touch at room temp, before adding the cheesecake layer.
While carrot cake is cooling, prepare the cheesecake filling. In a large bowl, combine the cream cheese and erythritol using an electric hand mixer, until smooth and creamy. Add in the vanilla, sour cream, and heavy cream and mix until well combined.
Add the egg, and mix just until combined. Be careful not to over mix the egg, as it will change the texture of the cheesecake.
Pour this mixture into the pan, on top of prepared carrot cake.
To bake in the instant pot:
Wrap the cheesecake with foil – crimping around the edges so that it stays secure.
Pour 1 1/2 cup of water into the inner liner of your instant pot and place the trivet in the bottom, keeping the handles folded up.
Fold a large piece of aluminum foil (about 2 feet) 4 times to make a sling that you will use to lift the cheesecake out of the IP when it's done cooking.
Lay the sling out, and set the cheesecake on top of it, centered. Gather up the two ends and carefully lift the pan, and set it into the instant pot. Leave the sling in place, just folding the edges over.
Secure the lid on your instant pot and set the steam vent to the sealing position.
Press “manual” and then the + or – button to adjust the time to 30 minutes. (make sure it is set to HIGH pressure)
When the cooking cycle ends, allow pressure to naturally release and carefully remove cheesecake from pot using the sling.
Leave it covered for about 30 minutes, then carefully peel off the foil. Let it sit at room temp for about 1 hour, then refrigerate for about 4 hours before serving or removing from springform pan (tough, I know!)
For baking in the oven:
Preheat oven to 400°F. Place a large pan filled with 1/2 inch of water in the oven.
Carefully place cheesecake into the preheated water bath in the oven. Bake for 10 minutes, then turn the oven down to 350°F and bake for 25-30 minutes or until top is browned and the cheesecake is only slightly jiggly. Remove from oven and allow to sit at room temp for 1 hour, then in chill in the refrigerator for at least 4 hours before serving or removing from springform pan.
For the optional topping:
Combine all of the ingredients except the pecans in a small bowl. Once they are well combined, microwave for 10-15 seconds making the frosting pourable.
Once cheesecake is cooled, pour the frosting over the top and spread into a thin, even layer.