Preheat the oven to 250F. Line a rimmed sheet pan with a piece of parchment paper long enough to hangover the sides.

Cut the tomatoes in half. Scatter them onto the prepared pan. Drizzle with the oil. Season with salt, as desired, and top with thyme.

Roast for 1 1/12 to 2 hours, turning halfway through, until the tomatoes are collapsed and softened.

Let cool completely. Transfer to a container, and add more oil until the tomatoes are completely covered. Packed this way, the tomatoes will keep for up to 2 months in the fridge.