Preheat your oven to 350° F. Line a 6-inch round baking pan with parchment paper. Toast your chopped pecans by placing them in a small skillet over low heat. Allow them to cook until they are toasted and fragrant, around 3 minutes, tossing them in the skillet every 30 seconds or so, to avoid burning. Chop into small pieces using a knife or food processor. Set aside.
In a large mixing bowl, sift and whisk together the flour, almond flour, sea salt, baking powder, baking soda, and ground cinnamon.
In a large mixing bowl, add your aquafaba and silken tofu. Whisk together (or use a hand mixer) until the silken tofu has been completely broken down and the mixture is frothy. Then, add your brown sugar and applesauce. Again, whisk until creamy. Then, add the vegetable oil slowly and down the side of your bowl, whisking constantly as you add it, until you achieve a very creamy mixture (around 2 minutes if using a hand mixer and 7 to 8 minutes if whisking by hand). Finally, add your vanilla extract in the same way you added your vegetable oil.
Add your dry ingredients, along with the carrot and the toasted pecans, to your bowl of wet ingredients. Using a spatula, incorporate the dry ingredients in large circular motions around your bowl, until all the dry ingredients have been incorporated. Do not overmix. Pour your batter into your prepared baking pan and bake until a toothpick inserted in the center comes out clean (around 38 to 40 minutes). Allow the cake to cool completely. (You can even wrap it in plastic wrap and place it in the fridge overnight--doing so will make frosting much easier).
To make your frosting, using a hand mixer, combine vegan cream cheese, butter, sugar, condensed milk, and sour cream until smooth and creamy. Set aside. Then, using the whisk attachment to a stand mixer, whisk your heavy cream on high into stiff peaks (mine takes about 1 minute). Add one heaping spoonful of the cream cheese mixture and whisk until incorporated. Continue adding cream cheese mixture, one large spoonful at a time, until it is entirely incorporated.
Once your cake has completely cooled, slice your cake in half (to create two cake layers--you can also skip this and just frost the top!). Using a spoon or a piping bag, add a enough frosting on top of the bottom layer so that it is entirely covered. Gently place the second layer on top. Add frosting to the top and, using your spoon or an offset spatula, smooth out the top and frost the sides. Decorate the top of your cake with more toasted pecans.
Optional: To make small marzipan carrots, add 1 tablespoon of almond flour and 1 teaspoon powdered sugar to two small bowls (each). Add to each bowl a couple drops of water, along with green and orange food coloring, respectively. Mix until a dough forms (drop by drop, keep adding water until you get a dough--don't add too much water, as it'll turn into a paste, not a dough!). Shape into small carrots and add to the top of your cake.