Preheat your oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan, or line with parchment paper leaving an overhang on the sides for easy removal. Set aside.

In your large mixing bowl, whisk together the vegetable oil, granulated sugar, brown sugar, eggs, and 1 teaspoon of vanilla extract until well combined and smooth.

Add the all-purpose flour, baking soda, ground cinnamon, 1/2 teaspoon salt, and ground nutmeg directly into the wet ingredients in the same bowl. Whisk until just combined. Be careful not to overmix; a few lumps are fine.

Using a rubber spatula, gently fold in the grated carrots and chopped pecans or walnuts (if using) until evenly distributed throughout the batter.

Pour the batter into the prepared baking pan and spread evenly. Bake for 30-35 minutes, or until a wooden skewer inserted into the center comes out clean.

Remove the cake from the oven and let it cool in the pan for 10-15 minutes before carefully transferring it to a wire rack to cool completely. The cake must be entirely cool before frosting.

In a separate medium bowl, using an electric mixer (or whisk vigorously by hand), beat the softened cream cheese and softened butter together on medium speed until light and fluffy (about 2-3 minutes).

Gradually add the sifted powdered sugar, 1 teaspoon vanilla extract, and 1/8 teaspoon salt. Start on low speed to avoid a sugar cloud, then increase to medium-high and beat until smooth and creamy, about 2-3 minutes. If the frosting is too thick, add a tablespoon of milk or cream; if too thin, add more powdered sugar.

Once the cake is completely cool, spread the cream cheese frosting evenly over the top. Slice and serve.