Heat your oven to 350°F/175°C. Spray two round cake pans with vegetable spray. You can also place a piece of parchment paper at the bottom of the pans and spray the sides with vegetable oil.*
Combine in a large mixing bowl the flour, Swerve, peanut butter powder, salt, cinnamon, pumpkin pie spice, and baking soda. Stir to combine. Set aside.
Place walnuts on a baking pan and toast for 5 minutes. Be careful not to cook too long because they will burn. Remove from the oven and allow to cool before chopping. Stir walnuts into the flour mixture.
In a smaller bowl combine the vegetable oil, applesauce, water, vinegar, and vanilla. Stir to combine.
Add the chopped carrots to a food processor and pulse several times to shred the carrots. Pour the shredded carrots into the vegetable oil mixture. Stir to combine. Pour this into the flour mixture. Stir until combined.
Pour the batter into your prepared pans. Bake for 35 minutes until a toothpick inserted in the middle comes out clean.
Allow the cake to cool for about 10 minutes before inverting onto plates. Allow the cakes to cool completely.
In the meantime make your Vegan Cream Cheese Frosting. Place cauliflower florets in a microwave-safe bowl and microwave for 1 to 2 minutes until tender. Add the hot, tender florets to the bowl of a food processor, and add the vegan cream cheese, Swerve, and chia seeds. Pulse until smooth (chia seeds will still be apparent). Set aside to allow the chia seeds to thicken.
Ice the top of one of the cakes. Place the second cake on top. Cover the top cake with frosting. Optional: Garnish with chopped walnuts.
Store this cake in an airtight container or wrapped in plastic wrap or foil in the fridge for up to 3 to 5 days.