Turn your stove to medium heat and add the oil to your skillet or Dutch oven. Once the oil is hot, add the garlic and Trinity (green bell pepper, celery, and onion). Cook for around 3-4 minutes, stirring often, until soft.
Now add the cabbage and sausage, stir, and cook it down for around 5 minutes.
Time to add the chicken broth and the seasonings and stir well.
Bring to the boil on medium-high heat, and then reduce the heat to a low simmer and cover. Simmer for around 1 hour. Take a peek every once in awhile, giving it a stir during your checks. If the mixture looks dry at anytime, you can add a bit of extra broth.
After 1 hour, remove the lid and increase the heat to medium. Cook uncovered an extra 10 minutes to boil off the liquid. At the end of cooking time, taste and adjust the seasonings by adding more Cajun seasoning, salt, and/or pepper to your tastes.
