Preheat the grill to high. Whisk together 1 tablespoon of the oil and 1 teaspoon of the vinegar. Brush over the tuna steaks and lightly season with pepper. Set aside to marinate while you prepare the vegetables.
Put the capsicums, skin-side up, on a grill tray and grill for 5 minutes or until the skins are blackened and blistered. Put them in a plastic bag and leave until cool enough to handle, then, working over a bowl to catch the juice, peel them. Cut into dice and add to the juice in the bowl. Add the tomatoes.
Heat a heavy, non-stick frying pan, add the tuna steaks and cook over a medium–high heat for 1 minute on each side until lightly browned but still very rare in the middle. Remove from the pan and set aside.
Heat the remaining oil in the pan and gently cook the onion for 5 minutes until soft. Add the chilli, garlic, cinnamon and sugar and stir for a few seconds, then tip in the capsicums, tomatoes, green beans, remaining vinegar and water. Bring to the boil, then cover and simmer for 3 minutes. Stir in the olives and place the tuna steaks on top of the salsa. Cover and cook for 3–4 minutes until the tuna is cooked to your liking and the beans are just tender.
Transfer the tuna to warmed plates. Stir the mint into the salsa and bubble for a few seconds, then stir in half the basil. Spoon the salsa over and around the tuna, scatter over the remaining basil and serve.