Rip the pedicels off, washing the tomatoes very well and leaving them to dry.
Cut each tomato into two halves and remove the green part, also known as the pith.
Squeeze the two halves of the tomato in a bowl or in a sink, to get rid of all the seeds.
Once you’ve repeated this process with all the tomato halves, put them in a steel pot, and cook the tomatoes on a stove’s hotplate, on low heat, turning them occasionally with a spoon, until dry and disintegrated.
Now pass the tomatoes through a food mill. Once all tomatoes have been passed, transfer the resulting sauce in a smaller steel pot while you will again put on the hotplate.
Add salt and oil to the sauce, and let it simmer over high heat, until you get the desired thickness.
Then turn off the heat and add the whole basil leaves to the sauce or coarsely chopped by hand.
If the tomatoes that you purchased are not particularly tasty, you can add to the sauce a fried onion or garlic to make the sauce more delicious.