Preheat an oven to 200°F (93°C).

In a medium bowl, combine the egg, milk, salt, and pepper and beat until well blended. In another medium bowl, combine the flour and cornmeal.

In a heavy, deep skillet over medium-high heat, pour the oil to a depth of ½ in (12 mm) and heat to 350°F (180°C) on a deep-fry thermometer. Dip the tomato slices in the egg mixture to coat evenly. Then dip in the cornmeal mixture, shaking off any excess and wiping your hands to avoid build-up. Fry the tomatoes in 3 batches, turning once, until the coating is crisp and light golden brown on both sides, a total of 3-5 minutes per batch.

Working quickly with a slotted spatula, transfer the tomatoes to a baking sheet lined with paper towels to drain. Then transfer the tomatoes to a baking sheet lined with aluminum foil and place in the warm oven until all the batches are ready to serve. Sprinkle with salt and pepper and serve warm.

Garnish with thyme sprigs, if desired.