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 and shake well.

Open the jar and add the olive oil. Seal again and shake until combined. Set aside.

In a medium bowl, combine 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 romaine, radicchio, and remaining dressing. Season with salt and pepper.

Add half of the chickpea and vegetable mixture and toss to combine. Top the salad with the remaining chickpea and vegetable mixture, extra black pepper, and vegan 'parmesan' if desired. Serve immediately.