Bring a large pot of water to a boil. Add salt. Drop the pasta into the boiling water; stir to keep pasta from sticking together. Cook until al dente according to package directions.
Meanwhile, heat olive oil in a large saucepan over medium-low heat. Add garlic and chiles, and cook for 1 minute, being careful not to let it brown. Stir in parsley, lemon zest, salt, and pepper; cook for 1 minute. Add cockles, and stir until well coated; cover tightly. Increase heat to medium high, and cook just until cockles begin to open, 4 to 6 minutes.
Sprinkle cockles with vinegar, and cook, uncovered, until vinegar has evaporated, about 1 minute.
When pasta is done, drain it, and transfer to a large platter. Remove cockles from broth, and place on pasta. Cook broth for 1 minute more. Remove from heat, and spoon broth over cockles. Serve immediately, garnished with basil.