In a pot of boiling water, blanch tomatoes. Drain and refresh in ice water. Drain. Peel, core, cut into quarters, and remove seeds.
Line a baking tray with parchment paper and arrange the tomato quarters on the tray, cut side down. Drizzle generously with olive oil. Sprinkle with thyme and garlic.
In a small bowl, combine salt, pepper and sugar, and sprinkle evenly over the tomatoes.
Bake until the tomatoes begin to shrivel, about 1 hour.
When the tomatoes are cool enough to handle, transfer to a container. Pour olive oil over and cover the container.