Prepare a pressure canner and jars for hot pack canning. Heat the canner water to about 180°F.

Roast the red bell peppers under a broiler, on a grill, or over an open flame until charred on all sides. Place them in a covered bowl to steam for 10–15 minutes. Once cooled, peel off the skins, remove the seeds, and chop the peppers.

Dice the carrots and onions, and chop the tomatoes if using fresh. Combine the chopped roasted peppers, carrots, onions, tomatoes, garlic, smoked paprika, black pepper, and your choice of liquid (water, tomato juice, or broth) in a large stockpot. Add salt to taste.

Bring the mixture to a boil over medium-high heat, then reduce to a simmer and cook for 5 minutes.

Ladle the hot soup into prepared, hot jars, leaving 1 inch of headspace. Remove air bubbles, adjust headspace if needed, wipe the rims clean, and apply two-piece canning lids.

Process jars in a pressure canner at 10 pounds pressure for weighted gauge canners or 11 pounds pressure for dial gauge canners, adjusting for altitude. Process pints for 75 minutes and quarts for 90 minutes.

After processing, turn off the heat and allow the canner to cool and depressurize naturally. Remove jars and let them sit undisturbed for 12–24 hours. Check seals before labeling and storing in a cool, dark place.