Use smaller eggplants, which are less bitter. Look for eggplants with a small, round dimple versus the deep, long groove in the bottom.
Whisk together eggs and 1 Tbsp. water until blended.
Cut tomatoes into 16 (1/8-inch-thick) slices. Place tomatoes in a single layer on paper towels.
Dredge eggplant in 1/2 cup crushed tortilla chips; dip in egg mixture, and dredge in remaining 1 1/2 cups crushed tortilla chips.
Cook eggplant, in batches, in hot oil in a 10-inch (3-inch-deep) skillet over medium heat 3 to 4 minutes on each side or until golden brown. Place on a wire rack, and sprinkle with salt and pepper to taste.
Cut cheese rounds in half. Arrange eggplant, cheese, and tomatoes on a serving platter; sprinkle with basil, and drizzle with balsamic vinegar. Sprinkle with salt and pepper to taste.