Preheat the oven to 200°C.
Blanch the tomatoes in boiling water for 1 minute, then drain, cool, and peel. Using a knife tip, open the ends gently and squeeze out seeds and excess juice.
Make caramel by melting sugar cubes with water in a saucepan until golden. Pour into a thick-edged small springform pan and let harden.
Melt butter in a sauté pan and sear tomatoes until foamy. Add powdered sugar and split, scraped vanilla pods. Cook 5 minutes, then drain in a colander for 20 minutes, reserving juices and pods.
Arrange tomatoes and vanilla pods on the caramel. Top with puff pastry, tucking edges neatly between tomatoes and pan sides.
Bake at 180°C for 35 minutes until crust is golden. Invert onto a wire rack to cool.
Reduce reserved tomato juices to a syrup and drizzle over the tart. Serve warm with vanilla ice cream.
