Preheat oven to 425 degrees.
Use a sharp paring knife to core the tomatoes. Cut tomatoes in half; transfer to one large (or two smaller) rimmed baking sheet; add onion, carrots, garlic and thyme.
Toss tomato mixture with oil; season generously with salt and pepper. Spread in a single layer (turn tomatoes cut side down). Toast until tender, 45 minutes to 1 hour. If vegetables begin to brown too quickly, push them toward the center of the sheet.
Using tongs or your fingers, peel off tomato skins; discard. Transfer mixture (including juices) to a blender; pulse several times until chunky. Let cool completely; transfer to an airtight container.