Slice your green tomatoes into ½-inch thick rounds. Place them on a paper towel-lined plate and sprinkle lightly with salt. Let them sit for 10 minutes to draw out excess moisture.
Pat the tomato slices dry thoroughly with paper towels after resting.
Set up your dredging station: In the first shallow bowl, place the flour seasoned with ¼ teaspoon each of salt and pepper. In the second bowl, whisk together the buttermilk and beaten eggs. In the third bowl, combine cornmeal, breadcrumbs, Cajun seasoning, and the remaining salt and pepper. If using Parmesan, add it to this final mixture.
In a large, heavy-bottomed skillet (cast iron works best), heat oil to a depth of approximately ¼ inch. The ideal temperature is 350°F (177°C).
Working with one slice at a time, dredge each tomato first in the seasoned flour, then dip in the egg-buttermilk mixture, and finally coat thoroughly in the cornmeal mixture. Press gently to ensure the coating adheres well.
Carefully place 3-4 tomato slices in the hot oil, being careful not to overcrowd the pan. Fry for 2-3 minutes on each side until golden brown and crispy. Use a slotted spatula to flip and remove them.
Transfer the fried tomatoes to a wire rack set over a baking sheet. While still hot, sprinkle with a touch of flaky sea salt if desired.
Continue with remaining tomato slices, maintaining oil temperature between batches.
Serve immediately while hot and crispy.