Preheat oven to 250°.

Cut the tomatoes lengthwise in half and remove the seeds by poking them out with your fingertip. Toss the tomato halves with the oil, salt, sugar, and thyme in a large bowl. Spread the tomatoes in a single layer, cut-side up on a baking sheet and bake for about 3 to 4 hours. The tomatoes should be slightly brown on the edges, the skins wrinkled, and have the texture of a soft prune.

Can be made ahead and refrigerated, but bring to room temperature before serving.