Jambalaya is a Creole dish with influence from West African, French, and Spanish cuisine. It's similar to other rice and meat dishes common in Louisiana cuisine. Gumbo typically includes Gumbo Filé Powder or Okra and is served over rice which is cooked separately. Étouffée is a stew which always includes shellfish, but not sausage. Like Gumbo, it's typically served over rice which is cooked separately. In jambalaya, the rice is "jumbled" or "mixed up" with the dish.
Prepare ingredients coarsely chopping celery stocks, red and green bell peppers, and green onions. Dice the bacon. Prepare smoked sausage and Andouille sausage by halving lengthwise, then cutting into 1/2" pieces. Cut smoked ham or tasso into 1/2" cubes. Cut chicken thighs into 1" pieces. Position rack in bottom third of oven and preheat to 350°F.
Cook bacon in very large pot over medium-high heat until brown but not yet crisp, stirring often, 8 to 10 minutes.
Add smoked sausage, andouille, and tasso. Sauté until meats start to brown in spots, about 10 minutes. Add onions, celery, and bell peppers. Cook until vegetables begin to soften, stirring occasionally, 10 to 12 minutes.
Mix in chicken. Cook until outside of chicken turns white, stirring often, 5 to 6 minutes. Mix in paprika, thyme, chili powder, and cayenne powder. Cook 1 minute. Add diced tomatoes with chiles and broth; stir to blend well. Add more cayenne, if desired. Mix in rice.
Bring jambalaya to boil. Cover pot. Place in oven and bake until rice is tender and liquids are absorbed, 45 to 48 minutes. Uncover pot. Remove from oven. Mix in chopped green onions.
Sprinkle jambalaya with chopped parsley and serve immediately.