Heat the oil or butter in a large skillet over medium heat. Add the flour and whisk constantly, creating a roux that turns a blonde color over about 10 minutes. This aromatic base will develop a nutty scent and a golden hue.
Add the chopped onion, bell pepper, and celery to the roux. Stir frequently, cooking until the vegetables are soft and translucent—about 5-7 minutes. You’ll hear them sizzle and see their edges becoming tender.
Stir in the minced garlic and paprika, cooking for another 1-2 minutes until fragrant. The garlic should smell sweet and aromatic, and the paprika will deepen the color of the mixture.
Pour in the broth and add the bay leaf. Bring to a gentle simmer, stirring occasionally. Let it cook for about 10 minutes to allow the flavors to meld and the sauce to thicken slightly.
Stir in the crawfish tails, ensuring they are immersed in the flavorful sauce. Reduce the heat to low and simmer for another 8-10 minutes, until the crawfish are tender and heated through. The sauce will become rich and slightly thickened.
Season with hot sauce, salt, and pepper to taste. Remove the bay leaf. Stir gently so the crawfish tails remain whole and are coated in the sauce.
Serve the crawfish etouffee hot over fluffy cooked rice. The sauce should be thick, glossy, and vibrant with a warm, spicy aroma. Enjoy the hearty, flavorful dish immediately.