Cut the tomatoes in half or quarters, and remove the stems. Put these in a processor for food. Puree them in lots, and pour the puree into a big pot.
Sprinkle the salt over the tomato puree and heat it uncovered over medium high heat until the tomatoes release juice and start boiling. Hold to boil for about 30 minutes.
When heating, remove the foams that you will see on top.
Reduce heat to medium low, and allow the puree to simmer for about 40 minutes until it has a consistency. Let them cool down.
Put a strainer over a large bowl. Pour the cooled tomato sauce into the strainer. Press down the sauce using a spoon until only the seeds and the skin remains in the strainer.
Pour the sauce into thin layer in one or two baking sheets. Wait for 3-4 days under the sun depending on the temperature, until it gets really dense.
You can then put the tomato paste into jars after this duration.
Transfer the paste into clean jars using a spoon, pressing it down well each time you put a spoon. Flatten the surface and pour olive oil on it. Tighten up the jar lid. Store it away from sunlight, either in the refrigerator or in your pantry.