Preheat the oven to 200°C/400°F/Gas 6.
Place the tomatoes in the frying pan with the vegetable oil, salt and pepper and honey or sugar. Arrange together as tightly as possible. Sprinkle the tomatoes with the breadcrumbs – this will soak up some of the juice which comes out of the tomatoes during cooking. On a well-floured work surface, roll out a circle of puff pastry the same size as the top of the frying pan. Place the puff pastry over the tomatoes, tucking it around them so the tomatoes are encased.
Brush the pastry with the lightly beaten egg on the top only. It does seem a bit pointless as this will be the underneath of the tart, but I like that bit of extra crunch that it adds to the pastry and it looks so much more presentable for that minute before you turn it upside down!
Bake in the oven for 20 minutes, or until the puff pastry is well puffed and golden brown. Remove from the oven and leave to sit for a few minutes, then tip away the excess liquid (if any) and put a large plate upside down on top of the frying pan. Using oven gloves, press the plate down hard and then quickly flip the whole thing so the frying pan is upside down and the plate is on the bottom. I do this over the sink because there is usually some leakage!
Remove the frying pan. Once the tart is cold, rip up some mint or basil leaves and drizzle with extra-virgin olive oil. Add salt and pepper if required. Serve cold with cold meats, cheeses, olives or salads.