makes one 8 or 9-inch square cake.
Preheat oven to 425°F and spray interior of an 8 x 8-inch (or 9x9) baking pan with baking spray (or grease it with coconut oil or butter).
In a large bowl, whisk together the flour, cinnamon, baking powder, baking soda, and salt. Add the grated carrots and nuts and stir to evenly distribute.
In a 4-cup liquid measuring cup or medium bowl, whisk the eggs into the Greek yogurt then add the coconut oil, syrup, and vanilla. (Good tip from Kate: If the coconut oil solidifies on contact with the cold ingredients, gently warm the mixture in the microwave in 30-second intervals until it melts again, or let the measuring cup/bowl rest in a warm place for a few minutes.)
Pour the wet ingredients into the flour/carrot bowl and stir with a spatula or spoon until combined. Pour batter into prepared pan and bake until the center of the cake springs back when lightly touched, about 35 minutes for an 8" square, less for 9" (like 26–28 minutes). Keep the cake in the pan and cool on a rack.
For the frosting:
Using an electric mixer, combine the cream cheese and butter until smooth. Add the powdered sugar and vanilla and mix on high until smooth and creamy. Use to frost a cool cake.