Preheat the oven to 250 degrees. Place the cherry tomatoes on a large rimmed baking sheet and toss with 1 tablespoon of the olive oil, basil, salt, and pepper. Turn each tomato top side up and spread in a single layer.

Roast for 2 – 2.5 hours (depending on the size) or until the edges are dried but the insides are still juicy, checking for doneness after 2 hours. Cool on a wire rack, then place in an air tight container, tossing with the remaining 1 tablespoon of olive oil to preserve.