Preheat oven to 180°C and grease your cake pan.
In a large bowl, mix flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
In another bowl, whisk sugar, melted coconut oil, milk, vinegar, and vanilla.
Add wet ingredients to dry ingredients and mix gently until combined.
Fold in grated carrots and chopped walnuts.
Pour the batter into the prepared pan and smooth the top.
Bake for 30–35 minutes or until a toothpick comes out clean.
Cool the cake completely on a rack before frosting.
For frosting, beat vegan cream cheese, butter, powdered sugar, and vanilla until smooth and fluffy.
Spread frosting generously over the cooled cake.
Garnish with extra walnuts or a sprinkle of cinnamon for flair.