In a medium stockpot, bring the shrimp stock to a boil. Reduce the heat to medium-low and simmer until reduced to 3 cups, about 25 minutes. When reduced, remove from the heat.
Meanwhile, fill a large stockpot three-fourths full with salted water and bring to a boil. Plunge the lobster headfirst into the boiling water and cook, covered, for 7 minutes. Transfer with tongs to a large bowl filled with ice water to cool. When the lobster is cool enough to handle, crack the shell, and remove the meat from the tail and claws. Discard the shells. Roughly chop the meat and set aside.
Bring a large pot of water to a boil. Add 1 teaspoon of salt and the pasta and cook, stirring occasionally, until al dente, about 8 minutes. Drain in a colander and return to the pot. Toss with 1 tablespoon of oil and 1/4 cup of the piri piri sauce.
Meanwhile, heat the remaining 4 tablespoons of olive oil in a large saute pan over medium-high heat. Add the chorizo, and cook, stirring occasionally, until brown, about 4 minutes. Add the shallots and garlic, and cook, stirring, for 1 minute. Add the tomato, shrimp, and Essence, and cook, stirring, until the shrimp start to turn pink, about 2 minutes.
Once the shrimp start to turn pink, add the clams, mussels, the remaining 1/4 cup of piri piri sauce, the reduced shrimp stock, 1/2 teaspoon of salt, and 1/2 teaspoon of black pepper. Cover the pan and simmer until the clams and mussels open, about 5 minutes. Add the oysters and the chopped lobster, and cook, stirring, until the oysters start to curl around the edges, about 2 minutes. Discard any unopened clam or mussel shells.
To serve, place the pasta in the center of a large platter, and arrange the seafood around the edges. Pour the broth over the pasta, garnish with the cheese and basil, and serve immediately.
Yield: 4 servings