Preheat the oven to 350°F.

Grease a 9x5-inch loaf pan and line the bottom and two sides with a piece of parchment paper, leaving a slight overhang.

In a large mixing bowl, whisk together the brown sugar, vegetable oil, melted butter, cinnamon, nutmeg, ginger, and salt. Add the eggs, and whisk until fully combined.

Switch to a silicone spatula and add the flour, baking powder, and baking soda, gently stirring until the batter is mostly combined. It’s okay if there are still a few streaks of dry flour.

Add the grated carrots and chopped walnuts and stir just until distributed through the batter and no dry streaks of flour remain.

Pour the batter into the prepared loaf pan and smooth the top with the spatula. Bake until a toothpick inserted into the center of the loaf comes out clean, 50 to 60 minutes.

Let the carrot loaf cool in the pan on a wire rack for 10 minutes. Run a butter knife along the two unlined ends of the cake, then use the parchment overhang like a sling to pull the cake out of the pan. Set the cake on the wire rack to cool completely.

While the cake cools, make the cream cheese frosting. In a medium bowl, use a hand mixer or a whisk to beat the cream cheese and butter until fully combined and smooth, about 1 minute. Add the powdered sugar and vanilla extract and mix until smooth and creamy, about 1 minute.

When the cake has cooled completely, use a small offset spatula or the back of a spoon to spread the frosting on top of the cake, making decorative swoops and swirls. Sprinkle the top with a handful of chopped toasted walnuts.