Heat the oil in an iron skillet on top of the stove or in the oven for a few minutes. Whisk together the cornmeal, flour, sugar, baking powder, baking soda and salt. Stir in the eggs, mayonnaise, shredded cheese, pimentos and buttermilk.
Pour into heated skillet and bake in preheated 425 degree oven for 25 to 30 minutes until brown on top.
Notes
You could make this cornbread as muffins or in a round baking dish.