Preheat your oven to 400°F (200°C).
Slice the eggplants into ½-inch thick rounds.
Sprinkle the eggplant slices with salt and let them rest for 30 minutes.
Brush both sides of the eggplant slices with olive oil.
Arrange the slices on a baking sheet in a single layer.
Roast the eggplant for 25-30 minutes, flipping halfway through.
While the eggplant roasts, prepare the bread by toasting it lightly.
Spread hummus generously on one side of each toasted bread slice.
Layer roasted eggplant, tomato slices, and arugula on top of the hummus.
Drizzle with balsamic vinegar if desired, then top with another slice of bread.
Cut the sandwich in half and serve immediately.
