Slice the eggplant into thin rounds, approximately 1/8 inch thick. Sprinkle lightly with salt and let sit for about 30 minutes to draw out moisture. Rinse and pat dry.

Slice the zucchinis into thin rounds, similar to the eggplant slices.

In a skillet, heat 2 tablespoons of olive oil over medium heat. Cook the eggplant slices in batches for 3-4 minutes on each side until golden brown. Remove and drain on a paper towel.

In the same skillet, add another 2 tablespoons of olive oil and sauté zucchini slices for 2-3 minutes on each side until slightly tender but still crisp. Remove from heat.

Whisk together the remaining olive oil, balsamic vinegar, minced garlic, lemon juice, salt, and pepper in a small bowl to create a dressing.

Arrange the eggplant and zucchini slices on a serving platter in an overlapping pattern. Drizzle the dressing over the vegetables.

Top with torn basil leaves and sprinkle with Parmesan cheese if using. Let sit for 10 minutes before serving.