Heat a large heavy-bottomed pot or Dutch oven over high heat, add the oil and heat through. Whisk the flour into the hot oil to make the roux. Lower the heat to medium-low and continue to whisk until the roux becomes a deep brown color, about 10 minutes.
Add the onions, celery, bell pepper, jalapeño and garlic, cooking until the vegetables become soft, about 6 minutes.
Add the tomato then add the thyme, paprika, and cayenne, stirring to combine and cooking for about 1 minute.
Stir in the shellfish stock, stirring to combine. Bring the mixture to a boil, then reduce the heat to medium-low and simmer, stirring occasionally, until the mixture thickens, about 10 minutes.
Add the crawfish tails and stir in the Worcestershire, hot sauce and cream. Season with salt and pepper.
Ladle the mixture into soup bowls and top with a scoop of the rice. Garnish with green onions and parsley.
Notes
For a smoother sauce, strain the roux and sautéed vegetables through a fine-mesh sieve before adding the crawfish and stock; this removes lumps and ensures a silky, restaurant-style texture without altering flavor.