Preheat the oven to 250 degrees F. Line a baking sheet with parchment or foil.
Arrange the tomatoes, cut side-up, in a single layer on the prepared baking sheet. Sprinkle with 1 teaspoon salt and scatter with the thyme sprigs. Bake until the tomatoes are slightly shriveled but still plump, about 5 hours.
Use the roasted tomatoes right away or layer with fresh thyme sprigs in a resealable container and cover with oil. Refrigerate for up to 2 weeks.
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