Step 1: Heat a large Dutch oven or a heavy-bottomed pot over medium-high heat. Add 1 tablespoon of olive oil. Once shimmering, add the sliced smoked sausage. Cook, stirring occasionally, until the sausage is nicely browned and has rendered some of its fat, about 5-7 minutes. Remove the sausage with a slotted spoon and set aside, leaving the rendered fat in the pot.
Step 2: Add the remaining 1 tablespoon of olive oil to the pot, if needed. Add the diced onion, green bell pepper, and celery (the "holy trinity"). Sauté, stirring frequently, until the vegetables are softened and translucent, about 8-10 minutes.
Step 3: Stir in the minced garlic, Cajun seasoning, smoked paprika, dried thyme, and black pepper. Cook for 1 minute more, stirring constantly, until fragrant. Be careful not to burn the garlic.
Step 4: Add the shredded green cabbage to the pot. It might seem like a lot, but it will cook down significantly. Stir well to combine the cabbage with the seasonings and vegetables. Cover the pot and allow the cabbage to cook down for about 10-15 minutes, stirring occasionally, until it has wilted considerably.
Step 5: Pour in the chicken broth and add the bay leaf. Bring the mixture to a simmer, then reduce the heat to low. Cover the pot again and let it simmer for 20-30 minutes, or until the cabbage is very tender.
Step 6: Return the browned smoked sausage to the pot. Stir in the apple cider vinegar and season with salt to taste. Allow it to simmer uncovered for another 5-10 minutes, letting the flavors marry and the liquid reduce slightly.
Step 7: Remove the bay leaf before serving. Garnish with fresh chopped parsley, if desired. Serve hot and enjoy this comforting dirty cabbage recipe!