Preheat oven to 350°F (175°C). Grease two 9-inch round pans.
Whisk together flour, baking soda, cinnamon, salt, and nutmeg.
In another bowl, mix oil and sugar. Beat in eggs and vanilla.
Combine wet and dry mixtures gently. Fold in carrots and walnuts.
Divide batter into pans. Let rest 15 minutes before baking.
Bake for 25–30 minutes until a toothpick comes out clean.
Cool in pans for 10 minutes, then on racks completely.
Frost with cream cheese frosting or serve plain.