Core the tomatoes and slice them in half top to bottom. Scoop out the seeds and arrange cut side up on a rimmed baking sheet. Sprinkle with part of the salt and pepper.

Roast until very soft and starting to dry out, about 45 minutes. Peel the roasted tomatoes and coarsely chop.

Warm the olive oil in a large pot and cook the onion, garlic, and remaining salt and pepper over medium heat until fragrant but not browned, 8 to 10 minutes.

Add the white wine and simmer until most of it evaporates, about 10 minutes. Add the roasted tomatoes, stock, and basil.

Cook until heated through, about 20 minutes. Meanwhile, preheat your pressure canner.

Blend the soup completely smooth with an immersion blender, or work in batches in a standing blender. Return to the pot and bring back to a simmer.

Ladle the hot soup into prepared jars, leaving 1 inch headspace. Remove air bubbles, wipe the rims, and add lids and bands fingertip tight.

Process pints for 50 minutes or quarts for 60 minutes at 10 lbs pressure in a weighted gauge canner or 11 lbs in a dial gauge canner, adjusting for altitude. Use a natural pressure release and never force cool the canner.