Place the tomatoes in a large pot or bowl. Pour boiling water from a kettle over the tomatoes, ensuring they are fully submerged. Leave them for 10-15 minutes or until the skins start to break.
Remove the tomatoes from the water, peel off the skins, and chop the tomatoes, removing the hard white middle part as well.
Heat the olive oil in a large, heavy-bottomed pot over medium heat. Add the chopped tomatoes to the pot. Stir in the salt and dried oregano. Bring the mixture to a boil, then reduce the heat to low and let it simmer gently for 1-2 hours, stirring occasionally, until most of the liquid has evaporated and the sauce has thickened to your desired consistency.
If you are working with a large amount of tomatoes, the reduction process may take longer. To speed up the process, consider using multiple pots. Wider pots provide more surface area for evaporation, helping the sauce to reduce more quickly.
Sterilize the jars and lids by boiling them in water for at least 10 minutes. Keep them hot until ready to use.
Ladle the hot tomato sauce into the sterilized jars, leaving about 1/2 inch of headspace at the top. Wipe the rims of the jars clean, place the lids on, and screw on the bands until they are finger-tight.
Place a cloth or dish towel at the bottom of a large pot to prevent the jars from making direct contact with the pot. Arrange the filled jars on top of the cloth and fill the pot with hot water, making sure the water level reaches halfway up the sides of the jars. Bring the water to a boil, then reduce to a low simmer. Let the jars simmer gently for 40-45 minutes.
Carefully remove the jars from the pot and place them upside down on a towel or rack. Cooling them upside down helps to create a strong seal. Allow the jars to cool completely.
Once cooled, check that the lids have sealed properly. Store the sealed jars in a cool, dark place. The sauce can be kept for up to 12 months. Once opened, refrigerate and use within 5-7 days.