Wash crabs under cold running water to remove sand. Using long-handled tongs, drop crabs, several at a time, into a large pot of boiling water. Cover and cook until the shells are bright red, about 5 to 10 minutes. Remove crabs and set aside to cool. Repeat with remaining crabs.
Break off crab claws; crack and set aside. Place each crab on its back. Remove and discard the small piece at the lower part of the shell that terminates in a point (the apron). Remove the fat beneath the apron and set aside. Holding the crab in both hands, insert your thumb or a blunt knife under the shell by the apron hinge. Remove and discard the top shell. Remove the spongy substance (the gills) that lies under the tapering points on either side of the crab back. Set the crab body aside.
Combine oil and flour in a large, heavy pot or Dutch oven and cook over medium-low heat, stirring constantly, until roux is the color of peanut butter, about 30 minutes (see Eula Mae's roux).
Stir in tomatoes, sugar, onions, bell peppers, celery, and garlic, and mix well. Cook, stirring often, until vegetables are soft, about 5 minutes. Add tomato paste, tomato sauce, tomatoes with chiles, and water and stir until well blended. Simmer, uncovered, for 10 minutes, stirring frequently. Add crab fat, TABASCO® Sauce, cayenne, bay leaves, salt, and black pepper. Cover and simmer 2 to 2 1/2 hours, stirring occasionally; sauce should be thick like a stew.
Add crab claws; cover and simmer 5 minutes. Add crabs; cover and simmer 10 minutes. Stir in the shrimp and simmer, covered, for 30 minutes, stirring occasionally.
Remove from heat, uncover, and let stand 10 minutes. Serve over rice.
Makes about 15 servings.
Recipe from "Eula Mae's Cajun Kitchen Cookbook"