Preheat the oven to 220°.
Slice the tomatoes in half and place them on a baking sheet, cut side up. Drizzle with the olive oil and sprinkle the salt and chile molido over the top. Place the tomatoes in the oven and cook for 1 ½-2 hours until the tomatoes have lost their moisture. They should be soft and slightly chewy. Remove from the oven.
Increase the oven temperature to 425°.
Place the puff pastry on another baking sheet. Place the tomatoes on the puff pastry, leaving a small border along all the edges. Slice the green chile into strips and add to the tomatoes then crumble the goat’s cheese on top.
Place the baking tray in the oven and bake the tart for 15-20 minutes until the pastry is lightly browned and the cheese warm and melted. Slice into squares and serve hot or at room temperature.