Place the first four pesto ingredients in a food processor and pulse until well combined but not creamy. Season to taste, add the Parmesan, and pulse once or twice more to blend.
Heat the oven to 375°. Pat dry the fish fillets and sprinkle them with salt and pepper. In a medium bowl, toss together the zucchini, shallot, and pesto until well blended.
To prepare each fillet, center it on a short end of a sheet of parchment, a few inches from the edge. Top it with one quarter of the pesto-veggie mixture. Fold the parchment in half over the fish. Fold in a corner of the creased edge to seal it. Working around the perimeter of the packet, make another overlapping fold, then continue in this manner, overlapping as you go, until the packet is completely sealed.
Place the pouches on a large baking sheet and bake until the fish is opaque, about 11 minutes (thick fillets may take slightly longer). Transfer the contents of each pouch to a dinner plate.