If using fresh puréed tomato, make the purée as per directions in Recipe Notes.
If using fresh puréed tomato, take that purée and put half in a large pot, bring to a rapid boil over high heat, stirring frequently. Add remaining purée a cup at a time, so that you don't lose the boil. This is to help prevent separation of tomato solids and water.
If using passata, just empty jars into in a large pot, bring to a boil.
Regardless of your starting base, add all remaining ingredients to pot.
Bring back to a boil.
If using fresh puréed tomato, boil hard uncovered stirring frequently, until you have the consistency of ketchup: 15 to 25 minutes.
If using passata, simmer lively uncovered until you have the consistency of ketchup: about 10 minutes.
Remove pot from heat
Ladle sauce into heated jars.
Leave 2 cm (1/2 inch) headspace.
Debubble, adjust headspace.
Wipe jar rims.
Put lids on.
Process in a water bath or steam canner.
Process jars for 35 minutes; increase time as needed for your altitude.