Pour oil into a large pan.
Place pan over medium heat.
When oil is hot and shimmering, add tasso ham and Andouille sausage. Saute until just starting to brown.
Add onion, celery, bell pepper and garlic. Saute 15 minutes, stirring occasionally.
Add Louisiana Spice. Mix.
In a medium bowl, add tomatoes, tomato sauce and bay leaves. Mix well. Add mixture to pan. Cook 10 to 15 minutes, stirring occasionally.
Add green onions, water and chicken base. Lower heat to low and simmer 45 minutes.
Use immediately or refrigerate, in a sealed container, until ready to use. (Sauce is actually best when made a day or more in advance.) Before serving, pick out and discard bay leaves.