In a large cast iron or ovenproof skillet, arrange the tomatoes cut-side up and drizzle with oil; toss with your hands to coat them well, rearrange them in a single layer (don’t worry about them being closely packed; they will shrink quite a bit as they cook), and sprinkle with salt and pepper. Roast for an hour at 400°F (alternatively, you could slow roast them for 4 hours at 250°F).
If you slow roasted your tomatoes, turn the oven up to 400°F. If your puff pastry is in a block, roll it out to approximately the same size as the pan you’re using. Crumble the goat cheese over the roasted tomatoes and top it with the puff pastry, crimping the edges underneath with your fingers (sloppy = rustic) or trimming the corners off to make a circle with a paring knife.
Bake for 20 minutes, until the puff pastry is golden. Let sit for 10 minutes, then turn out onto a serving dish; retrieve any goat cheese that has stuck to the bottom of the pan and put it back onto the tart. Cut into wedges to serve.