Make the sauce. Heat a large, dry nonstick frying pan until hot, add the shallot and cook for 2 minutes. Add the tomatoes and cook for a further 2 minutes, then add the chilli and continue to cook for 2–3 minutes until starting to char. Stir in the garlic and cook until all the vegetables are lightly charred. Leave to cool slightly, then remove the blackened skin from the tomatoes and chilli. Transfer the flesh to a food processor or blender with the shallot and garlic and whizz to a coarse purée.
Heat the oil in saucepan, add the vegetable purée, oregano, vinegar and a little water if necessary and simmer for 10 minutes until thickened. Season well.
Meanwhile, heat a little oil in a small nonstick frying pan, add one-quarter of the eggs, season and swirl around the pan, then cook for 1–2 minutes until just set. Fold the omelette in half, slide on to a plate and keep warm. Repeat with the remaining eggs.
Spoon a little of the sauce over each omelette and serve sprinkled with the feta.