Preheat oven to 350°F/180°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.*
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.
Combine in a large mixing bowl the flour, sugar, salt, cinnamon, pumpkin pie spice, and baking soda. Stir to combine. Stir half of the walnuts into the flour mixture. Set aside.
Add the chopped carrots to a food processor and pulse several times to shred the carrots. Add the vegetable oil, water, vinegar, and vanilla to the food processor and pulse in quick bursts to combine.
Pour the carrot mixture in with the flour mixture. Stir to combine, making sure there are no clumps of flour throughout the batter.
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 a serving plate. Allow the cakes to cool completely.
In the meantime make your Vegan Cream Cheese Frosting by combining the vegan cream cheese and vegan butter in a mixing bowl. Mix until light and fluffy. Add the powdered sugar 1/2 cup at a time. Then add the lemon juice and beat until you get a spreadable consistency. If it's too thick, you can add a tablespoon of plant-based milk.
Ice the top of one of the cakes. Top with additional chopped, toasted walnuts. Place the second cake on top. Cover the top cake and sides with frosting. Garnish with chopped walnuts.