Turn your stove to medium high and add oil to your skillet. Once hot, add the sausage and cook (stirring often) until the sausage is a light brown color (about 5-10 minutes). Remove the sausage and place on paper towels to drain. At this point you can remove some of the drippings but I like to leave this in for extra flavor!
Turn down the heat to medium and add the garlic and Trinity (green bell pepper, celery, and onion). Cook for around 3-4 minutes, stirring often.
Now add the cabbage, stir, and cook it down for around 5 minutes. Then return the sausage to the skillet and add the chicken broth and a pinch of each of your seasonings.
Bring to the boil, and then reduce the heat to a simmer and cover. Simmer for around 30 minutes, checking every 10 minutes or so and giving it a stir. At the end of cooking time, taste and adjust the seasonings by adding more Cajun seasoning, salt, and/or pepper to your tastes.