Make the pesto. In a food processor add garlic, nuts, and olive oil, pulse until garlic is broken down. Add parmesan, lemon juice, salt, pepper and basil leaves. Pulse keeping texture, not completely smooth.
Warm Chickpeas. Place chickpeas in a pan with salted water or broth. Warm gently with a lid on for a few minutes, just enough to steam and soften the chickpeas. Drain excess liquid (or leave it, up to you!). Let cool a minute or two. (You can skip this step and just use chickpeas cold or at room temperature.)
Combine. Add chickpeas to a large bowl, toss with pesto, tomatoes, kalamata olives, and red onions.
Season. Taste, adjust salt and lemon juice to taste.
Garnish with a squeeze of lemon, toasted pine nuts, fresh basil leaves, and a sprinkle of parmesan or vegan parmesan.
