Wash canning jars in hot soapy water and keep warm in a low oven (170°F/77°C) or dishwasher. Fill your canner with water per manufacturer instructions and set new lids in hot (not boiling) water to soften the sealing compound.
Score an X in the bottom of each tomato, blanch in boiling water for 45–60 seconds until skins split, then transfer immediately to an ice bath. Once cool, peel, halve, core, and roughly chop the tomatoes — squeezing out excess seeds for a thicker soup.
Blend onions, celery, garlic, and basil until finely minced, then transfer to your large stockpot. Blend chopped tomatoes in batches until smooth (or slightly chunky), adding each batch to the pot.
Stir in sugar, salt, and pepper, then bring to a gentle simmer over medium heat. Cook on low for 20–30 minutes, stirring occasionally, until the mixture reduces by about one-quarter. Use an immersion blender or food mill for a silkier texture if desired.
Remove warm jars one at a time and add 2 tbsp bottled lemon juice (or 1/2 tsp citric acid) to each quart jar using a canning funnel. This step is essential for safe canning and must not be skipped.
Ladle hot soup into each jar leaving 1 inch of headspace, then run a bubble remover tool around the inside edge to release air. Wipe the rims clean, center a lid on each jar, and screw on a band until fingertip-tight.
Secure the canner lid, heat on high until steam vents for 10 minutes, then add the weight and bring to 10 lbs pressure (weighted gauge) or 11 lbs (dial gauge). Process quart jars for 25 minutes, then turn off heat and allow pressure to return to zero naturally before opening.
Ensure jars are covered by at least 1 inch of water, bring to a rolling boil, and process quart jars for 40 minutes (start timing once water returns to a full boil). Adjust processing time for altitude above 1,000 ft per USDA guidelines.
Lift jars onto a towel-covered counter and leave undisturbed for 12–24 hours. Check seals by pressing the center of each lid — it should not flex. Label with contents and date, then store in a cool, dark place for up to 18 months.