Heat the tablespoon of extra virgin olive oil in a large, heavy-bottomed stockpot or Dutch oven over medium heat until it shimmers.
Drop the diced yellow onion, sliced celery, carrots, and green bell pepper into the hot oil. Sauté the vegetables for 5 to 6 minutes, stirring frequently with a wooden spoon, until the onions turn soft and translucent.
Stir in the minced garlic, dried oregano, dried basil, smoked paprika, and cayenne pepper. Cook the spice matrix for exactly 60 seconds until highly aromatic, taking care not to let the garlic scorch.
Add the chopped green cabbage pieces directly into the pot. It will look like a massive volume of greens, but it will rapidly wilt down as it heats through. Stir for 2 to 3 minutes to coat the cabbage in the spices and warm oil.
Pour in the full can of crushed tomatoes with their juices, followed by the 6 cups of vegetable broth. Stir the entire mixture thoroughly to integrate the base.
Turn the stovetop heat up to medium-high and bring the soup to a rolling boil.
Once boiling, immediately reduce the heat to medium-low, slide a lid onto the pot slightly ajar to allow excess steam to escape, and let it simmer gently for 25 to 30 minutes. The soup is finished when the cabbage matrix is completely fork-tender and translucent.
Turn off the heat completely. Pour in the tablespoon of fresh lemon juice and season the broth lightly with salt and black pepper to preference.
Ladle the hot soup into deep bowls and serve immediately. Store any leftovers in an airtight container inside the refrigerator for up to 5 days, or freeze in portioned containers for easy meal prep.