In a medium bowl, whisk 1/2 cup of the flour with the cornmeal, Cajun spice, and 1/2 teaspoon salt. Put the remaining 1 cup flour, buttermilk, and the cornmeal mixture respectively in 3 shallow dishes. Season the buttermilk with hot sauce, to taste.
With the flat side of a cook's knife or the smooth side of a meat-pounder, pound each breast to equal thickness. Pat the chicken breasts dry and season with salt.
Lightly coat each breast in flour and shake off any excess. Dip each breast into the buttermilk to coat and remove, shaking slightly so the excess buttermilk drains back into the bowl. Dredge the chicken in the cornmeal mixture, shaking off any excess coating. Lay the chicken on a piece of waxed paper.
Heat a large (12-inch) cast iron skillet over medium heat with about 1/2 inch of oil. Lay 2 chicken breasts smooth-side down in the pan and cook until golden brown, 3 to 4 minutes. Flip and cook 3 to 4 minutes more. Drain chicken on a paper towel. Repeat with remaining chicken.
Place all chicken breasts on a rack over a baking sheet and bake until firm to the touch, 6 to 8 minutes. Season with salt, and serve immediately with mustard mayonnaise or sliced tomatoes.
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