Bring the reserved shrimp shells and 4 1/2 cups water to a boil in a stockpot or large saucepan over med-high heat.
Decrease heat to med-low and simmer for 20 minutes.
Strain the stock and add the clam juice and ice water (you should have about 2 quarts of tepid stock, 100 to 110 degrees); discard the shells; set the stock aside.
Heat the oil in a Dutch oven or large heavy-bottomed saucepan over med-high heat until it registers 200 degrees on an instant-read thermometer, 1 1/2 to 2 minutes.
Decrease the heat to medium and gradually stir in the flour with a wooden spatula or spoon, working out any lumps that form.
Continue stirring constantly, reaching into the edges of the pan, until the mixture has a toasty aroma and is deep reddish brown, about the color of an old copper penny or between the colors of milk chocolate and dark chocolate, about 20 minutes (the roux will become thinner as it cooks; if it begins to smoke, remove the pan from the heat and stir the roux constantly, to cool slightly).
Add the onions, bell pepper, celery, garlic, thyme, salt, and cayenne to the roux and cook, stirring frequently, until the vegetables soften, 8-10 minutes.
Add 1 quart reserved stock in a slow, steady stream while stirring vigorously.
Stir in the remaining stock.
Increase the heat to high and bring to a boil.
Decrease heat to medium-low, skim the foam off the surface, add the bay leaves, and simmer, uncovered, skimming any foam that rises to the surface, about 30 minutes.
Stir in the sausage and continue simmering to blend the flavors, about 30 minutes.
Stir in the shrimp and simmer until cooked through, about 5 minutes.
Off the heat, stir in the parsley and scallions and adjust the seasonings with salt, pepper, and cayenne to taste.