Preparation: Start by prepping all your ingredients: chop the onion, bell pepper, and celery; slice the Andouille sausage; and mince the garlic. Also, measure out the Cajun or Creole seasoning, thyme, and chicken broth.
Cook the Sausage: In a large Dutch oven or pot over medium-high heat, sauté the Andouille sausage slices until they start to brown. Remove them from the pot and set aside.
Sauté the Vegetables: In the same pot, add the diced onion, bell pepper, and celery. Cook until the vegetables start to soften, about 5 minutes. Stir in the minced garlic and cook for another 1-2 minutes on medium heat so the garlic doesn't burn.
Season: Add the Cajun or Creole seasoning and fresh thyme to the vegetables, stirring to evenly distribute the spices.
Pasta: Pour in the penne pasta and stir to coat it with the seasoned vegetables.
Liquids: Add the chicken broth and diced tomatoes (with their juice) to the pot. Stir well to combine all the ingredients.
Cook: Bring the mixture to a boil, then reduce heat to a simmer. Cover and cook for 12-15 minutes, or until the pasta is cooked to your liking.
Sour Cream: Once the pasta is done, remove the pot from heat and stir in the sour cream until well-mixed. If you're out of sour cream, you can also substitute whole milk, heavy cream, or half and half. Just reduce the amount by half.
Return Sausage: Add the cooked Andouille sausage back into the pot, stirring to incorporate.
Serve: Serve hot, garnished with additional thyme, parsley or green onions.