In a 4-quart heavy-duty saucepan, combine the scallion trimmings, celery trimmings, and onion trimmings with 5-1/2 cups of water; bring to a boil over high heat. Add the shrimp, let the water return to a boil, and cook until pink and cooked through, about 3 minutes. Remove from the heat and let sit for 3 minutes. Strain through a sieve set over a large glass measuring cup, reserving the stock. You will need 4-1/2 cups of stock, so add water if necessary. When cool enough to handle, peel and devein the shrimp. Discard the shells and trimmings.
Melt the butter in a 5- to 6-quart enameled cast-iron Dutch oven (or other heavy-duty pot) over medium-high heat. Add the celery, onion, and bell pepper and cook, stirring often, until softened, about 7 minutes. Add the ham and the reserved shrimp and cook, stirring often, until any excess moisture evaporates and the ham and vegetables begin to brown, about 5 minutes. Add the tomato paste and cook, stirring, until a shade darker, about 3 minutes. Stir in the bay leaf, thyme, cayenne, chili powder, allspice, cloves, and 1-1/2 tsp. salt. Stir in the rice. Add the reserved stock and bring to a boil. Cover, lower the heat to maintain a simmer, and cook, undisturbed, just until the rice is tender, 20 to 25 minutes. Check the rice for doneness in several places.
Remove the pot from the heat. Sprinkle the paprika over the jambalaya and, using a fork, gently fluff the scallions and paprika into the jambalaya. Cover and let stand for 10 minutes to let the flavors meld. Serve with hot sauce, if you like.
nutrition information (per serving):
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Photo: Scott Phillips