Make the pesto:
Combine all the pesto ingredients in a food processor with three or four ice cubes. If the mixture isn't creamy enough, add another ice cube and blend again. The pesto may be thick and a bit grainy—this is fine. Leave it in the processor, and just before draining the pasta, blend it again with a little pasta cooking water, adding gradually, until you reach your desired creaminess.

Make the clam sauce:
In a large skillet, sauté the garlic in the olive oil until golden (do not let it get too dark). Remove the pan from the heat for a couple of minutes, then add the clams. This brief wait helps lower the oil temperature so the clam shells don't crack when added. Cook the clams just until they open, then remove from heat immediately, as the pasta will finish cooking with the sauce.

The pasta will be tossed and finished over the heat, so the clams will finish cooking at that stage (if they are fully cooked now, they may dry out later). Remove the garlic and add chopped parsley. Shell most of the clams and return them to the sauce, reserving a few in their shells with a spoonful of sauce to use as garnish for each plate.

Cook the pasta until very al dente and reserve 1 cup of the cooking water. After draining, return the pasta to the pot over medium or high heat, depending on the amount of sauce and how cooked the pasta is. Add the heated clam sauce, then the pesto, and toss everything together with two large forks. If needed, add a little pasta cooking water to loosen the sauce. Check for doneness.

Divide among 6 plates and garnish with the reserved clams in their shells and a small sprig of parsley.