Prepare the pans. Preheat the oven to 350°F (175°C). Lightly grease two 9-inch (23 cm) round cake pans and line the bottoms with parchment paper.
Combine the dry ingredients. In a large bowl, whisk together the flour, baking powder, baking soda, salt, and cinnamon.
Mix the wet ingredients. In another large bowl, beat the brown sugar, vegetable oil, eggs, and vanilla with an electric mixer until smooth and well combined.
Finish the batter. Pour the wet ingredients into the dry ingredients. Mix gently just until no dry flour remains. Fold in the grated carrots and chopped walnuts until evenly distributed. Avoid overmixing.
Bake. Divide the batter evenly between the pans and smooth the tops. Bake for 30–35 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs.
Cool completely. Let the cakes cool in their pans for 10–15 minutes, then carefully turn them out onto a wire rack. Remove the parchment paper and allow both layers to cool completely.
Make the frosting. Beat the softened butter until pale and fluffy. Add the cream cheese and mix until smooth. Mix in the vanilla, then gradually add 4 cups (480 g) powdered sugar on low speed. Add more powdered sugar as needed, up to 5 cups (600 g) total. Scrape down the bowl and mix just until smooth and creamy.
Assemble. Place one cooled cake layer on a serving plate and spread frosting evenly over it. Add the second layer and frost the top. For my preferred method, assemble the cake in a deep cake pan lined with plastic wrap, leaving plenty of overhang to help with removal. The pan must be deep enough to hold both layers and the frosting.
Decorate and chill. Leave the sides uncovered for a rustic finish and sprinkle chopped walnuts over the top. Refrigerate for at least 2 hours to let the frosting firm up and the layers settle.
Serve. If assembled in a lined pan, carefully remove the chilled cake, peel away the plastic wrap, and transfer to a serving plate. If desired, spread reserved frosting over the sides. Cut into 12 slices, wiping the knife between cuts.