Lay the squid out on a chopping board. Slice open each tube so it lies flat, then lightly score a criss-cross pattern on the inside surface. Trim the tentacles if needed. A sharp kitchen knife like this makes it quick and precise. In a mixing bowl, combine the squid with the chopped garlic, smoked paprika, and 2 tablespoons of olive oil. Season with salt and white pepper, then toss well to coat. Set aside to marinate. A good set of nesting mixing bowls keeps everything tidy and organised. In a small bowl, whisk together the lemon juice and another 2 tablespoons of olive oil. A citrus juicer makes this easier and helps get every last drop. Place the whole peppers on a hot barbecue or, if cooking indoors, a cast iron griddle pan like this. Cook for around 10 minutes, turning regularly, until the skins are blackened and blistered all over. Transfer the peppers to a bowl, cover with cling film or a plate, and let them steam for a few minutes. Once cool enough to handle, peel off the skins, remove the seeds, and roughly chop the flesh into chunks.
In a large bowl, combine the chopped peppers with the halved cherry tomatoes, drained chickpeas, remaining 2 tablespoons of olive oil, sherry vinegar, and parsley. Season to taste with salt and pepper and mix everything together.
Place the squid in a single layer on the hottest part of the grill. Cook for 1–2 minutes on each side until it’s lightly charred and just tender. As each piece is done, transfer it straight into the lemon and olive oil dressing to rest and soak up the flavour.
To serve, spoon the chickpea and pepper mixture onto a serving platter. Add the grilled squid on top, scatter over the fresh basil, give everything a gentle toss, and serve immediately.