Preheat the oven to 350?F (175?C). Grease and flour the cake pan.

In a mixing bowl, whisk together the dry ingredients: flour, baking powder, baking soda, cinnamon, and salt.

In another bowl, combine the wet ingredients: oil, granulated sugar, brown sugar, and eggs. Mix until well combined.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

Fold in the grated carrots, chopped walnuts, and vanilla extract.

Pour the batter into the prepared cake pan.

Bake in the preheated oven for 35-40 minutes, or until a toothpick inserted into the center comes out clean.

Allow the cake to cool in the pan for 10 minutes before transferring to a wire rack to cool completely.