Preheat the oven to 350 degrees. Line an 8 1/2 inch x 4 1/2 inch baking loaf pan with parchment paper and set aside.
Add 1 1/2 cups all-purpose flour, 3 teaspoons baking powder, 1 teaspoon ground cinnamon, 1/4 teaspoon ground nutmeg, and 1/2 teaspoon salt to a large mixing bowl. Whisk until well combined and set aside.
Add 1 cup granulated sugar and 3 large eggs to another large mixing bowl. Whisk until well combined. Add 3/4 cup oil and 1 teaspoon vanilla extract and whisk until well combined.
Pour the dry ingredients into the bowl with the wet ingredients. Use a spatula to mix until just combined. Fold in 2 cups grated carrots (2-3 carrots) and 3/4 cup roughly chopped walnuts.
Pour the batter into the prepared loaf tin. Bake for 45 minutes, or until cooked through. Allow the cake to cool in the pan for 10 minutes before transferring to a cooling rack to cool completely.
Add 4 ounces cream cheese, softened, 2 tablespoons butter, softened, and 1/2 teaspoon vanilla extract to a large mixing bowl. Beat using handheld electric beaters until smooth and creamy.
Gradually add 2 cups powdered sugar and 1/4 teaspoon salt, and beat until well combined.
Spread the cream cheese frosting over the cooled cake before serving. Garnish with extra chopped walnuts if desired.
Notes
Cover the cake loosely with a sheet of foil if the top of the cake is browning too quickly before the cake has cooked through.
The loaf cake is cooked through if it springs back when lightly touched in the center. Alternatively, insert a skewer or toothpick into the center of the cake. If the skewer or toothpick comes out clean, the cake is cooked through.
This cake is also delicious served without frosting.