Heat the olive oil in a large frying pan and sauté the onion and garlic for 1–2 minutes. Add the aubergine and cook for 3–4 minutes, then add the courgettes and peppers, and cook over a low heat for 4–5 minutes.
Stir in the chopped tomatoes, bring to a simmer and cook for 2–3 minutes, until the vegetables start to soften.
Using a slotted spoon, divide the mixture between the pizza bases on 2 baking sheets. Top with the basil and grated mozzarella and bake in a preheated oven, 220°C (425°F), Gas Mark 7, for 11–13 minutes. Serve immediately.