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Step 1
Clean your shrimp under cold running water. Remove the head with a sharp knife, then de-shell the bodies. You'll be using the heads and shells as the flavor base of the stock. (Reserve the bodies for the cataplana!)
Step 2
Heat a large, deep saucepan or Dutch oven on the stove over medium-high heat. Coat the bottom of the pan with a thin layer of oil, then add the shrimp heads and shells and cook until browned. Add the onions, garlic, bay leaves, and saffron, sweating until the onions are soft but not browned. Add the butter and tomato paste, cooking for a minute or so, then cover with 2 quarts water. Heat to a simmer, and let bubble away (at a moderate, not aggressive) simmer, for about 30 to 45 minutes.
Step 3
Remove from the heat, add the parsley sprigs, and let stand for 15 minutes.
Step 4
Strain through a fine-mesh strainer, pressing on the solids to release all of their flavor. Discard the solids. You can use the stock immediately, refrigerate for up to 2 days, or freeze for up to 2 months.
Step 5
Soak your clams in a large bowl filled with ice and water for at least 15 minutes—this will help them release some of the sand in the shells. Then scrub and rinse under cold water.
Step 6
Heat olive oil in a cataplana pot (or a Dutch oven or other large pot with a tight-fitting lid) until shimmering, then add sausage and prosciutto. Brown, stirring occasionally, until the sausage gets a little color and the prosciutto starts to look like it’s crisping, about 5 to 7 minutes. Add the onions and pepper and continue to cook, stirring now and then, until the onions are soft but not brown, about 4 minutes. Add the garlic, and cook one minute more. Add the bay, pinch of saffron, paprika, tomatoes, and splash of white wine, stirring to deglaze the pan. Slowly add the shrimp stock, then cook at a low simmer for about 20 minutes, until the tomatoes lose their tinniness and all the flavors have sufficiently co-mingled.
Step 7
Increase the heat to bring to a boil, add in the shrimp and clams, lock the cataplana, and cook about 5 to 10 minutes, shaking occasionally. If using a Dutch oven, cook, covered, stirring occasionally until the clams pop open, 5 to 10 minutes. Once the clams have opened, slowly stream in the cream and stir, then shower with fresh parsley.
Step 8
Serve the cataplana right at the table, with bread, little fried potatoes, or white rice.