Preheat the grill to hot. Spread the peppers out, skin side up, on a baking sheet and brush over half of the oil.
Cook them under the grill for about 10 minutes, until the skins start to char, then turn over and brush the remaining oil over the pepper flesh.
Cook for a further 3–5 minutes, until the flesh starts to turn golden brown. Remove the peppers from under the grill and place the halves in a plastic bag. Leave the peppers to cool, then remove them and peel off the skins and discard.
Roughly chop the pepper flesh, reserving a few slices for garnishing.
Heat the butter in a saucepan. Add the onion and cook over a gentle heat for 7–10 minutes, until they start to soften but not colour. Then add the pepper flesh to the pan and cook for a further 2–3 minutes.
Crumble the stock cubes into the pan and pour in the water. Bring the mixture to the boil, then cover the saucepan with a lid, reduce the heat and simmer gently for 20 minutes.
Transfer to a blender or food processor and purée until smooth, in batches if necessary.
Season to taste and stir in the chopped basil just before serving. Garnish with pepper slices, basil leaves, and some freshly ground black pepper.
Serve with natural or Greek–style yogurt.