Preheat the oven to 400 degrees F (200 degrees C).
Place the tomatoes in the skillet with the vegetable oil, salt and pepper, and honey or sugar. Arrange together as tightly as possible. Sprinkle the tomatoes with the bread crumbs - this will soak up some of the juice which come out of the tomatoes during cooking. On a well-floured counter, roll out a circle of puff pastry the same size as the top of the skillet. 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 to 30 minutes, or until the puff pastry is well puffed and golden brown. Remove from the oven and let sit for a few minutes, then tip away the excess liquid (if any) and put a large plate upside down on top of the skillet. Using oven gloves, press the plate down hard and then quickly flip the whole thing so the skillet is upside down and the plate is on the bottom. I do this over the sink because there is usually some leakage!
Remove the skillet. Once the tart is cold, rip up some basil or mint leaves and drizzle with extra-virgin olive oil. Add salt and pepper if required. Serve cold with cold meats, cheeses, olives, or salads.