Preheat oven to 425 degrees F.
Toss cherry tomatoes and garlic cloves with olive oil, salt, and pepper. Spread on a baking sheet and roast for 20-25 minutes or until lightly charred.
Combine roasted tomatoes and garlic with chickpeas, basil, tahini, lemon juice and reserved canned chickpea liquid in a blender or food processor. Blend until smooth and season with salt and pepper.
Increase oven temperature to 500 degrees F.
Heat saute pan over medium heat. Add chorizo and cook until browned, breaking it up with a wooden spoon into smaller chunks. Remove from heat.
Assemble pizzas. Spread hummus on naan and top with smoked mozzarella, crumbled chorizo, red onion, and sliced peppadew. Place pizzas on sheet pans and bake for 4 minutes or until cheese is melted and lightly browned.
Meanwhile, make arugula salad. Toss arugula with chopped olives, parsley, oregano, feta, olive oil, and red wine vinegar. Season with salt and pepper.
Remove pizzas from the oven and top with arugula salad. Serve immediately.