In a large bowl, whisk garlic, oil, vinegar, lemon zest, lemon juice, honey, mustard, oregano, and red pepper; season with salt and black pepper.
Make Ahead: Dressing can be made 5 days ahead. Store in an airtight container and refrigerate. Bring to room temperature and whisk to combine before using.
Add Brussels sprouts and onion to bowl with dressing and toss well to combine. Let sit at room temperature, tossing occasionally, until sprouts and onions marinate and soften in dressing, at least 20 minutes or up to 1 hour.
Add tomatoes, mozzarella, salami, roasted peppers, provolone, olives, peperoncini, half of Parmesan, and three-quarters of basil; season with salt and black pepper. Top with remaining Parmesan and basil.
