Heat your oven to 350°F (175°C) and lightly coat a 9×13-inch baking pan with cooking spray or a thin layer of oil.
In a large mixing bowl, combine the flour, baking soda, baking powder, cinnamon, nutmeg, and salt, whisking until evenly blended.
In a separate bowl, beat the eggs, brown sugar, granulated sugar, vegetable oil, and vanilla extract until smooth and creamy.
Slowly fold the dry mixture into the wet ingredients until everything is just combined. Be careful not to overmix, which could make the cake heavy.
Stir in the grated carrots and walnuts. The carrots add incredible moisture, and the walnuts bring a subtle crunch.
Spread the batter evenly into the prepared pan, then gently smooth the surface with a spatula.
Bake for 40 to 45 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool completely before spreading a generous layer of cream cheese frosting on top.
