With the rack in the highest position, preheat the oven’s broiler. Line a baking sheet with aluminum foil.
Place the cherry tomatoes, cut side up, on the prepared sheet. Drizzle with the oil. Sprinkle with the cheese and sugar. Season with salt and pepper. Cook under the broiler for about 5 minutes or until tomatoes begin to caramelize and burst.
When ready to serve, sprinkle with chives. Spoon over tomato risotto (see recipe).