Step 1

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.

Step 2

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.

Step 3

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.