Make the dressing. In a sealable jar, combine the red wine vinegar, thyme, pepperoncini pepper brine, vegan mayonnaise, agave nectar, Dijon mustard, Tamari, garlic, salt, and pepper. Seal the lid on top of the jar and shake well. Add the olive oil, seal again, and shake. Set aside.

In a medium bowl, combine the chickpeas, cherry tomatoes, red onion, cucumber, pepperoncini peppers, olives, and sun dried tomatoes. Season with salt and pepper and toss with 3 tablespoons of the dressing.

In a large serving bowl, combine the romaine, radicchio, and remaining dressing. Season with salt and pepper. Add half of the chickpea and vegetable mixture and toss to combine. Top with the remaining mixture, extra black pepper, and vegan "parmesan" if desired. Serve immediately.