Preheat the oven to 325°. Cover a sheet pan with parchment paper or foil.
Wash and core the tomatoes. Cut them in half through the equator. Very large tomatoes may need to be quartered,
Spread the tomatoes cut side up on the sheet pan. Drizzle liberally with olive oil and sprinkle with salt and pepper. Roast for about 2½ hours, or until the tomatoes are nicely dehydrated and jammy.
Use the tomatoes immediately or pack into a clean glass jar and tap the jar on the counter to release any air bubbles. If you still see bubbles, run a chopstick or dinner knife around the inside of the jar until the bubbles are gone. Cover with more olive oil and store in the refrigerator up to three weeks.