Salt eggplant and place in colander to allow excess liquid to drain off.
Whisk together balsamic vinegar, ½ cup of olive oil, garlic, parsley, salt, and pepper in a medium bowl.
Add eggplant and toss to coat. Set aside for 10 minutes.
Brush a cast-iron stovetop grill pan with a thin layer of olive oil. Place over medium-high heat.
Grill eggplant until slightly charred, about 5 minutes per side. Set aside on a plate to cool.
Vinaigrette: Put red wine vinegar in a small bowl. Whisk in remaining ¼ cup of olive oil in a steady stream.
To build the napoleon, begin with a slice of eggplant, followed by a slice of Mozzarella, topped with a basil leaf. Repeat for a second layer.
Drizzle with vinaigrette and garnish with basil leaves. Scatter pine nuts around each napoleon and serve.