Preheat the oven to 425?F and bring a large pot of water to a boil. Cut an X in the bottom (not the stem end) of each tomato and blanch them for about a minute, plunging into cool water afterward and slipping off the skins. Cut them in half lengthwise and remove the seeds.
Set a heavy 9" cast iron skillet over medium high heat - add the butter to the pan and swirl it around as it melts and foams. Sprinkle the sugar evenly over the bottom of the pan and arrange the tomatoes rounded side down in concentric circles, fitting them tightly together and filling the pan (don't worry if you have leftovers). Place the skillet over medium heat and cook for 15-20 minutes, until the juices are released from the tomatoes, then bubble and cook down and turn golden. (Lift the tomatoes up occasionally and let the caramel run underneath them to keep them from sticking and burning.) Meanwhile, roll the pastry out to about a 9" round.
Remove the pan from the heat, drizzle the vanilla over the tomatoes and cover with the pastry, tucking in the edges (no need to be neat about it). Cut a few slits in the top and bake for about 20 minutes, until golden and bubbly around the edges. Cool for about 10 minutes before inverting onto a plate (do it while the tart and pan are still quite warm or the tomatoes will stick) - replace any that don't come out of the pan, and scrape any caramel and juices that have stayed behind over top.
Serve warm, with ice cream or whipped cream.