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1
Peel the shrimp and reserve the shells and heads.
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2
Refrigerate the shrimp and put the shells and heads in a large saucepan. Add the water, quartered onion, bay leaves, and 1 tablespoon of the salt. Bring to a boil, then reduce the heat to medium and simmer, uncovered, for 30 minutes.
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3
Remove from the heat and strain through a fine-mesh strainer.
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4
Discard the peelings and set aside the shrimp stock.
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5
Combine the oil and flour in a large cast-iron pot or enameled cast-iron Dutch oven over medium heat.
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6
Stirring slowly and constantly, make a roux the color of peanut butter, 15 to 20 minutes.
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7
Add the chopped onion, bell pepper, and celery and cook, stirring, until soft, 6 to 8 minutes. Add the shrimp stock and whisk to blend with the roux. Bring to a boil, then reduce the heat to medium-low and simmer, uncovered, for 1 1/2 hours.
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8
Add the shrimp, the remaining 1/2 teaspoon salt, and the cayenne and cook for 20 minutes.
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9
Remove from the heat and stir in the parsley.
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10
Ladle into individual soup bowls, garnish with the chopped eggs, and serve hot.
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11
Note: The stew can also be served over white rice.
