For the ratatouille tarts, roll the puff pastry out on a lightly floured work surface until it is 3mm thick. Line four 10cm/4in wide, 2.5cm/1in deep fluted loose-bottomed tart tins with the pastry, pressing gently into the edges.
Prick the base of the pastry several times with a fork. Place the tart cases in the fridge to rest for at least 30 minutes.
Preheat the oven to 190C/375F/Gas 5.
When the tart cases have rested, line each with baking parchment and fill with ceramic baking beans. Place the tart cases on a baking sheet and bake in the preheated oven for 15 minutes. Remove the parchment and baking beans and return the cases to the oven for another ten minutes. Gently press the pastry down if it rises in the centre.
Bake the tart cases until the pastry is cooked through and golden-brown. Remove the tart cases from the oven and allow to cool slightly before carefully removing them from the tins.
For the ratatouille, heat a pan until hot, then add the olive oil, onion and peppers and fry for 2-3 minutes.
Add the garlic, aubergine and courgette and fry for a further 2-3 minutes, stirring occasionally. Add the tomatoes and cook for a further minute. Add the basil leaves and season, to taste, with salt and freshly ground black pepper.
For the basil hollandaise, heat the butter in a heavy-based saucepan until foaming. Heat the lemon juice and vinegar in a separate small non-reactive pan until just boiling.
Place the egg yolks into a food processor with the salt and blend. With the motor running, add the hot lemon and vinegar mixture. Slowly, with the motor still running, add the melted butter in a thin, steady stream, until it is all incorporated and the sauce has thickened.
Place the sauce into a bowl, add the basil and season with a little salt, if needed, and the freshly ground black pepper.
For the poached eggs, crack an egg each into a small bowl. Heat a small pan of water over a medium het until just simmering. Swirl the water with a wooden spoon to create a vortex, then carefully drop the eggs in, two at a time.
Cook gently for 2-3 minutes, or until cooked to your liking. Carefully remove with a slotted spoon and drain onto kitchen paper.
To serve, place a tart shell into the centre of each plate. Divide the ratatouille equally among the tart cases. Top each with a poached egg and a spoon over the basil hollandaise.