Step 1

Preheat the oven to 350°F and then grease two 8-inch round cake pans and set aside. In a large bowl, combine all of the dry ingredients (brown rice flour to nutmeg) and sift together.

Step 2

In a separate large bowl, combine all of the wet ingredients (carrots to milk) and stir well. Add the dry ingredients to the bowl with the wet ingredients and use a spatula to gently fold together a few times. Pour in the walnuts and continue to fold with the spatula until everything is mixed together.

Step 3

Divide the batter equally into the two separate cake pans and bake in the oven for 35 minutes, or until you can prick the center with a fork and have it come out clean. Allow the cake to cool for several hours or overnight at room temperature, covered tightly.

Step 4

Meanwhile make the frosting by placing the cream cheese and Greek yogurt in a large bowl. Add 1/2 cup powdered sugar and then beat on high with a mixer for about 10 seconds, until smooth. Add the rest of the sugar along with the vanilla extract and continue to beat until the frosting is fluffy and smooth. At this point you can refrigerate the frosting overnight and ice the cake the next day, if desired.

Step 5

Once the cake is properly cooled, transfer it to a surface for icing. Using a spatula, spread a thick layer on top of the first cake, then place the second cake on top and spread on another thick layer, smoothing the excess over the edges. After the cake is completely covered in icing, you have the option to sprinkle the edges with chopped nuts for decoration or you can leave it as is. Serve immediately or refrigerate for up to 24 hours before serving. Store leftovers in an airtight container in the refrigerator for up to 3 days.