Step 1

In a stockpot, heat the oil. Add the shrimp shells and cook over high heat, until starting to brown, 5 minutes. Add the tomato paste and cook until it begins to stick to the pot, 2 minutes. Add the clam juice, onion, celery, carrot and bay leaves and bring to a boil. Simmer over moderately low heat for 25 minutes. Strain the stock into a heatproof bowl.

Step 2

In a saucepan, whisk the flour with the oil to make a paste. Cook over moderate heat, stirring often, until the roux turns golden brown, 30 minutes. Increase the heat to moderately high and cook, stirring, until the roux is dark brown, 10 minutes longer. Scrape the roux into a bowl and reserve.

Step 3

In the stockpot, heat 2 tablespoons of the oil. Add the garlic, onion and celery; cook over moderate heat, stirring, until softened. Add the roux and cook until bubbling. Stir in the stock and tomatoes and bring to a boil. Reduce the heat to moderately low. Simmer for 1 1/2 hours, until no floury taste remains; skim off the fat.

Step 4

In a skillet, heat the remaining 2 tablespoons of oil. Add the green pepper, okra, chile powder, paprika, filé, oregano, thyme, cayenne and white pepper. Season with salt and cook over moderately low heat, stirring, until fragrant, 5 minutes. Stir in a ladleful of the liquid in the stockpot, scrape up the browned bits and transfer to the gumbo in the pot. Simmer, stirring, for 1 hour.

Step 5

Add the shrimp to the pot and cook, until just white throughout, 2 minutes. Stir in the crab; season with salt.