Preheat the grill to medium-high heat.
In a large bowl, combine the zucchini slices, olive oil, garlic, balsamic vinegar, pepper, and salt. Toss to coat.
Grill the zucchini slices for 5-7 minutes, flipping halfway through, until they are lightly charred and tender.
Remove the zucchini from the grill and let cool slightly.
In a large bowl, combine the grilled zucchini, arugula leaves, and Parmesan cheese. Toss to combine.
Serve warm with a drizzle of balsamic vinaigrette.