Preheat the oven to 350F. Grease a 9x13 inch baking pan and line with parchment paper.
In a large bowl, whisk together the flour, baking soda, cinnamon, nutmeg, and salt.
In another bowl, beat the oil, granulated sugar, brown sugar, and eggs until well combined.
Pour the wet ingredients into the dry and stir until just combined. Fold in the grated carrots and pecans.
Spread the batter in the prepared pan and bake for 30 to 35 minutes, until a toothpick comes out with moist crumbs.
For the frosting, beat the cream cheese and butter until smooth. Add powdered sugar and vanilla, beat until fluffy.
Spread frosting over the completely cooled cake. Slice and serve.