To make homemade shrimp stock: this step is optional but absolutely worth it (especially if you purchased shrimp with the shells and tails left on).
Start by thawing the shrimp. Remove shells and tails. Transfer the shrimp to a large bowl and set aside to in the refrigerator until ready to use. Meanwhile, add the shells and tails to a large pot. Add the roughly chopped onion, bell pepper, celery, smashed garlic, and bay leaves. Fill with at least 8 cups of water.
Bring to a boil over high heat before reducing to low heat. Cover and simmer for 45-60 minutes. Strain the broth through a fine-mesh strainer into a separate pot or container and set aside.
You will only need approximately 3 cups of the stock to make this recipe. Save the leftovers in the refrigerator for up to 7 days or freeze for up to 4 months.
To make the roux: Melt your preferred fat (butter, vegetable oil, bacon drippings, or a mix) in a large, heavy-bottomed saucepan set over medium-low heat. Add the flour, whisking continuously to create a smooth mixture. Continue to cook, stirring continuously, for 10-15 minutes.
The color will turn from a creamy off white to a light caramel, to a deep, rich caramel color. Take care and watch the heat level as you do not want to burn the roux (otherwise you will need to start over). On the other hand, if the heat is too low, it will take forever, so set the heat somewhere between medium to medium-high and stir continuously.
Add and cook the "holy trinity": Once the roux has reached the desired doneness, add the finely chopped onion, green bell pepper, and celery to your roux. Mix well to combine. Cook over medium heat for approximately 8-10 minutes, stirring often. Add the minced garlic and continue to cook for an additional minute or so.
Stir in the shrimp stock (homemade or store-bought): Slowly add 3 cups of homemade shrimp stock to your roux-covered aromatics. Start with 2 cups, whisking well to incorporate, then add an additional cup as needed.
Etouffee is meant to be on the thicker side, so resist the urge to add too much stock too fast.
Season: Stir in the Cajun seasoning, paprika, plus salt and pepper, to taste. Allow it to cook for approximately 5 minutes, reducing heat to medium-low as needed and stirring frequently to prevent burning.
Add the shrimp: Add the thawed shrimp, mix to combine, cover and cook for approximately 5-10 minutes, or until shrimp are fully cooked.
You may also season your shrimp with a little Cajun seasoning and quickly sauté in a large skillet for approximately 5 minutes, tossing into the etouffee just before serving. Both options work - the later will result in a more flavorful shrimp.
Garnish and serve. Garnish with chopped parsley and green onions and serve with warm, fluffy cooked rice.