How to Make It
Put the parsley, capers, garlic, lemon juice, anchovy paste, mustard, 1/2 teaspoon of the salt, and the pepper into a food processor or blender. Pulse just to chop, six to eight times. With the machine running, add the 1/2 cup oil in a thin stream to make a coarse puree. Leave this salsa verde in the food processor; if necessary, pulse to re-emulsify just before adding to the pasta.
Light the grill or heat the broiler. Brush the zucchini with 1 tablespoon of the oil and sprinkle with 1/4 teaspoon of the salt. Grill or broil the zucchini, turning, until just done, about 10 minutes in all. When the slices are cool enough to handle, cut them crosswise into 1/2-inch pieces and put them in a large bowl.
Thread the shrimp onto skewers. Brush the shrimp with the remaining 1 tablespoon oil and sprinkle with the remaining 1/2 teaspoon salt. Grill or broil the shrimp, turning, until just done, about 4 minutes in all. Remove the shrimp from the skewers, slice them in half horizontally, and add them to the zucchini.
Meanwhile, in a large pot of boiling, salted water, cook the spaghetti until just done, about 12 minutes. Drain. Add the pasta to the grilled zucchini and shrimp and toss with the salsa verde.