Place tomatoes on paper towel–lined rimmed baking sheet. Cover with more paper towels, let sit for 20 minutes, and pat dry. Meanwhile, process 1/3 cup cornmeal in blender until very finely ground, about 1 minute. Combine processed cornmeal, remaining 1/3 cup cornmeal, flour, salt, pepper, and cayenne in shallow dish. Whisk buttermilk and egg together in second shallow dish.
Working one at a time, dip tomato slices in buttermilk mixture, then dredge in cornmeal mixture, pressing firmly to adhere; transfer to clean baking sheet.
Heat oil in 12-inch skillet over medium-high heat until 350 degrees. Fry 4 tomato slices until golden brown, 2 to 3 minutes per side. Drain on wire rack set in baking sheet. Bring oil back to 350 degrees and repeat with remaining tomato slices. Serve.
**TIP: To keep the tomatoes from weeping as they fry (which will loosen the coating), let them sit between paper towels for 20 minutes and then press dry.