In a large plastic food-storage bag, mix together the flour, garlic powder, salt, black pepper, and cayenne. Place the green tomato slices in the bag and shake until well coated.
Beat together the eggs with the buttermilk until well combined. Place the cornmeal on a plate.
Dip the flour-coated green tomatoes into the egg mixture then lightly dredge in the cornmeal. Place the cornmeal-coated tomatoes on a large plate or sheet. Repeat until all are done.
In a large heavy skillet heat 1/2 inch of oil on medium high to 350°F, about 5 minutes. If you don’t have a thermometer, you can test the temperature by sticking a wooden spoon into the oil. If it bubbles around the spoon, it should be ready for frying. Line a large plate or sheet with paper towels.
Working in batches, slide the tomatoes into the hot oil and cook for 1 minute then turn and cook for another minute or until golden. Remove with a slotted spatula to drain on the paper-lined plate.
Lightly salt the fried green tomatoes, then serve warm with buttermilk dressing.