If starting from fresh tomatoes, wash, core, and quarter them, then set aside.

Peel and chop the onion, and set it aside.

Peel and mince the garlic, and also set it aside.

Wash the basil, discard the stems, and mince it finely—set aside.

In a large pot, add the chopped onion, minced garlic, and oil.

Sauté the mixture until the onion starts to look clear.

If using fresh tomatoes, add the quartered tomatoes to the pot and cook uncovered for 20 minutes, stirring often.

Pass the mixture through a food mill or sieve to remove the skin and seeds. Return the strained tomato and onion purée to the pot.

If using passata, put the onion mixture in a food processor or blender, add some of the passata, and blend until smooth. Return to the pot and add the remaining passata.

Add the prepared basil to the pot.

If starting from fresh tomatoes, cook uncovered over medium heat until the volume is reduced by half—about 1 hour. For passata, simmer uncovered for 10 minutes.

Stir often to avoid scorching at the bottom of the pot.

To acidify the jars, add 1 tablespoon bottled lemon juice or 1/4 teaspoon citric acid to each half-litre jar, or 2 tablespoons lemon juice or 1/2 teaspoon citric acid to each litre jar.

Ladle the sauce into heated jars, leaving a 2 cm (1/2 inch) headspace.

Debubble the jars, adjust the headspace, and wipe the rims.

Put the lids on and process the jars in a water bath or steam canner. Process half-litre jars for 35 minutes and litre jars for 40 minutes. Increase the time as needed for your altitude.