Preheat the oven to 200°C. Cut the tomatoes in half horizontally, then place them, cut side up, in an ovenproof baking dish large enough to hold them in a single layer. Sprinkle with the salt.
Combine the breadcrumbs, Parmesan and oil in a small bowl, then sprinkle evenly over the tomatoes.
Bake for 25 minutes until the topping is golden and crispy and the tomatoes are cooked through.
Meanwhile, combine the vinegar and brown sugar with 1½ tablespoons of water in a small frying pan. Bring to the boil over a high heat and cook for 3 minutes until syrupy. Drizzle over the baked tomatoes and serve immediately.