Prepare the smoker for barbecuing, bringing the temperature to 200°F to 220°F.
Coat the tomatoes with 1 teaspoon of the oil. Transfer the tomatoes to the smoker. Cook them until they are very soft and the skins are ready to split, 45 to 55 minutes. Set the tomatoes aside until cool enough to handle. Coarsely chop the tomatoes with their peels.