Preheat the oven to 350°F (175°C). Grease and flour a 9×5-inch loaf pan.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, ground cinnamon, ground nutmeg, and salt. Set aside.
In a large bowl, beat the granulated sugar, light brown sugar, and eggs together until smooth and creamy.
Add the vegetable oil and 1 teaspoon vanilla extract to the sugar and egg mixture and mix until combined.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined.
Fold in the grated carrots and chopped walnuts until evenly distributed.
In a separate medium bowl, beat the softened cream cheese, 1/4 cup granulated sugar, egg, and 1/2 teaspoon vanilla extract until smooth and creamy.
Pour half of the carrot cake batter into the prepared loaf pan and spread evenly.
Spoon the cream cheese mixture over the batter and spread gently to cover.
Pour the remaining carrot cake batter over the cream cheese layer and spread evenly.
Using a knife or skewer, gently swirl the cream cheese layer into the carrot cake batter to create a marbled effect.
Bake in the preheated oven for 50 to 55 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs.
Remove the loaf from the oven and allow it to cool in the pan for 15 minutes.
Transfer the loaf to a wire rack and cool completely before slicing and serving.