Make the Roux:
Heat the oil in a large saucepan over medium-high heat.
Add the flour and cook, stirring constantly, until the mixture turns medium brown.
Add the butter and melt it in.
Sauté the Vegetables:
Add the yellow onion and cook until softened and barely brown around the edges.
Add the green onions, bell pepper, and garlic, and cook until tender.
Add the tomato and cook for a minute.
Simmer the Base:
Add 3 cups of water, the celery, parsley, basil leaf, and bay leaf.
Bring to a boil, then reduce heat and simmer for 10 minutes.
Add Crawfish and Seasonings:
Add the crawfish tails, crawfish fat (if using), Tabasco, salt, and pepper.
Simmer for 10-12 minutes more, adjusting seasonings to taste.
Serve:
Serve the étouffée over cooked white rice and garnish with chopped green onions.