Preheat oven to 400°. Start pesto: Toast nuts on a baking sheet in oven 4 to 5 minutes. Steam or simmer broccoli until tender-crisp, about 4 minutes. Drain, cool in ice water, and pat dry.
Pulse nuts, broccoli, parsley, garlic, and oil in a food processor until almost smooth. Add parmesan and salt; pulse to blend. Set aside.
Start salad: Combine onion, vinegar, salt, and pepper in a bowl; set aside.
Make pizza: Put naan on baking sheet; bake until lightly toasted, about 5 minutes. Brown sausage in a large nonstick frying pan over medium-high heat, breaking into chunks, 8 to 10 minutes. Spread naan with pesto, then arrange sausage, peppers, olives, and a layer of manchego on top.
Bake until cheese softens, 8 minutes. Add arugula and oil to vinegar mixture. Toss to coat; arrange over pizzas.
Note: Nutritional analysis is per serving.