Wash tomatoes, cut in half, place in large shallow noncorroding dishes or trays, sprinkle with salt, and set in direct sunlight for a few days, covered with cheesecloth to keep out insects and dust. Tomatoes will thicken slightly.
Put them through a small-holed colander set over a bowl, pressing against the tomatoes until only the seeds and skins remain in the colander. (A food mill may be used instead of a colander, but only if the tomato skins remain inside it.)
Put this creamy pulp into noncorroding trays again and place in sunlight covered with cheesecloth.
Stir every day for several days until the pulp is reduced to a paste.
Pour into clean jars, cover with a film of olive oil, and tie a piece of cheesecloth over the mouth of each jar.
The paste will keep for several months, all throughout the winter, at room temperature.