Preheat the oven to 400°F (200°C) and allow it to heat fully, about 5 minutes.
Slice each eggplant in half lengthwise and use a knife to score the flesh in a crosshatch pattern, being careful not to pierce the skin.
Brush the cut sides generously with olive oil and sprinkle with salt and black pepper to your liking.
Place the eggplant halves cut-side down on a baking sheet and roast for 20 to 30 minutes, until the flesh is soft and slightly caramelized at the edges.
Remove from the oven and gently press down the flesh with a fork to create a shallow, even surface for toppings.
Distribute the tomato sauce evenly over each eggplant half, using about 1 tablespoon per half.
Top each half with approximately 1/2 cup of shredded mozzarella, spreading it to cover the sauce.
Scatter the sliced black olives and halved cherry tomatoes over the cheese, then sprinkle with Parmesan if desired.
Return the baking sheet to the oven and bake for 8 to 12 minutes, until the mozzarella is completely melted and beginning to bubble slightly at the edges.
Remove from the oven and top with fresh arugula just before serving for a peppery, crisp contrast to the warm, cheesy eggplant.
