Preheat oven to 375 degrees. Slice tomatoes in half lengthwise and gently squeeze out seeds or scoop them with a spoon –leave as much as the flesh as possible.
Lay the tomatoes, cut side up, in a single layer on a rimmed baking sheet. Drizzle with the olive oil, balsamic vinegar and sprinkle with the thyme. Roast tomatoes on center rack for 40 minutes. Increase the oven temperature to 400 degrees and continue to roast tomatoes about 20 minutes more, or until caramelized.
Let tomatoes rest until reaching room temperature. The tomatoes will keep for up to 5 days in the refrigerator or for up to 6 months in the freezer.