extra-virgin olive oil (optional)
Preheat the oven to 300 degrees F. If your oven has a convection mode, preheat to 250 degrees F.
Cut the tomatoes in half lengthwise and remove the seeds completely. If your tomatoes are large, cut them into quarters to ensure even cooking.
Place the tomatoes, cut side up, on a rack set over a baking sheet. Sprinkle lightly with sea salt and bake for 1 hour. Turn the tomatoes over and return to the oven for another 1 1/2 hours. Then, turn the tomatoes cut side up once again and bake another 30 to 45 minutes, or until they're pliable but mostly dry. Turn off the oven and let the tomatoes sit until cool.
Cover with olive oil and refrigerate in a container with a lid for up to 1 month.
Note: Any variety of tomato works very well for this recipe: Roma, heirloom, your choice. The larger the tomato, the longer the cooking time will be. Convection ovens are perfect for this kind of recipe because the air circulates and speeds drying. Because the oven will be on for so long, maximize your yield by roasting two or three trays of tomatoes. This is easiest with convection, but it can be accomplished in a conventional oven by rotating the position of the trays periodically throughout cooking.