To make a roux, whisk together oil and flour in a large heavy saucepan (cast iron is perfect, but any heavy-bottomed pot or pan will do) over medium to medium-low heat. Once combined, it is easier to use a wooden spoon to stir. Stir continuously for at least 20 minutes, until mixture turns a dark caramel color. It should darken very slowly. If it darkens too fast, turn down the heat. The roux will burn if the heat is too high or you don't stir continuously. Be sure to really stir all the way up to the edges of the pot. You don't want any of the mixture to stay in one spot for too long.
Add onions, peppers, celery, jalapeno, and garlic. Cook, stirring frequently, until vegetables are tender, about 5 minutes.
Add tomatoes, broth, bay leaves, dried chili peppers, Cajun seasoning, salt and pepper. Bring to a boil. Reduce heat and simmer 25 minutes.
Meanwhile brown tasso ham in a pan using 2 tablespoons of vegetable oil.
Add pulled pork and tasso ham and simmer 5 more minutes. Check for seasoning and add more salt if needed. Remove and discard bay leaves and dried chili peppers.