Preheat oven to 350. Beat together oil, eggs and sugar and vanilla 3-5 minutes until creamy. In separate bowl, combine all dry ingredients, except carrots. Fold wet mixture into dry, then fold in carrots. Turn into greased, floured 9x13 pan. Bake 40-50 minutes at 350, until a toothpick inserted in center comes out clean.
Note: This is a very dense cake, and very moist, and may fall slightly in the center. If you're looking for more of a commercial type "light" carrot cake, this may not be for you. Also makes good muffins.