Preheat oven to 200°C/400°F/Gas 6. Unroll the pastry and cut a circle around a 25cm oven-proof frying pan.
Brush the pastry circle with the aubergine pesto and set aside.
In your frying pan, reduce the balsamic vinegar with the sugar. Let cool slightly before scattering the thyme and lemon zest over the balsamic reduction.
Arrange the tomatoes in single layers until the pan is full.
Drape the pastry circle over the top, tuck in the edges and bake in the oven for 20-25 minutes until crisp, puffed and golden.
Let the tart rest in the pan for 5 minutes; then place a large serving dish over the top and carefully flip the whole thing over to turn out.
Scatter over the crumbled dairy-free Greek- style cheese and serve immediately.
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