Chop all vegetables and mince garlic. Slice Andouille sausage. Rinse rice thoroughly under cold water until water runs clear; drain well. Peel and devein shrimp.

Heat olive oil in a large (5-6 quart) Dutch oven or heavy-bottomed pot over medium-high heat. Add sliced Andouille sausage and cook until nicely browned and some fat has rendered, about 5-7 minutes. Remove sausage with a slotted spoon and set aside, leaving rendered fat in the pot.

Reduce heat to medium. Add chopped onion, celery, and green bell pepper to the pot. Cook, stirring occasionally, until softened, about 8-10 minutes.

Stir in minced garlic, Cajun seasoning, dried thyme, dried oregano, black pepper, and cayenne pepper (if using). Cook for 1-2 minutes until fragrant, stirring constantly.

Pour in the diced tomatoes (undrained), chicken or seafood broth, Worcestershire sauce, and hot sauce. Add the bay leaves. Bring the mixture to a rolling boil, scraping any browned bits from the bottom of the pot.

Stir in the rinsed and drained long-grain white rice and return the browned Andouille sausage to the pot. Stir well to combine. Reduce heat to low, cover the pot tightly, and simmer for 20 minutes without lifting the lid.

After 20 minutes, gently fold in the shrimp and optional crawfish tails. Re-cover the pot and continue to simmer for another 5-10 minutes, or until the shrimp are pink and cooked through and the rice has absorbed most of the liquid and is tender. Do not overcook the shrimp.

Remove the pot from heat and let it rest, covered, for 5-10 minutes. This allows the flavors to meld and the rice to fully steam. Remove bay leaves. Taste and adjust seasoning with salt and pepper as needed.

Fluff the jambalaya with a fork. Garnish generously with fresh sliced green onions and chopped parsley before serving.