Pulse the walnuts in a food processor until finely ground. Be careful not to over-process the walnuts. They should still retain some of their texture.
Add one date at a time through the feed tube of the food processor while the food processor is running. The carrot cake mixture should be a little bit crumbly, but stick together when pressed in between your fingers. Finally, fold in the carrots.
Press the mixture into a greased 6" (15 cm) spring form. If you are using anything other than a spring form, line it with parchment paper for an easier removal. Place the carrot cake base in a freezer while you make the icing.
Add the cashews, coconut milk, melted coconut oil, maple syrup, lemon juice, vanilla and salt into a high-speed blender. Blend on high until the icing is smooth and creamy.
Remove the spring form from the freezer and spread the icing on top of the carrot cake base. Place the cake back into the freezer for about 4 hours to let the frosting firm up.
Once set, remove the cheesecake from the spring-loaded pan. Serve it frozen or let it thaw at room temperature for 10-15 minutes before serving.
Store leftover carrot cake in an airtight container in the freezer for 1-2 weeks.
*Squeeze out any excess juice from the carrots. If the carrots are too wet, they will make the cake too moist and dense.
**Soak the cashews in water for at least 8 hours (or overnight) so they soften up and are easy to blend. To quick-soak cashews, pour boiling hot water over the cashews and soak for 1 hour uncovered. When the cashews are done soaking, drain the water and rinse the cashews thoroughly. (Note: if you do the quick soak, the carrot cake will no longer be raw).
***Prep time does not include soaking the cashews (8 hours).