Rip off 4 sheets of parchment paper, each a little over a foot long.
Make layered stacks dividing the fennel, onions, garlic, olives, and cod among the parchment pieces, working in the center of each piece of paper. Season the cod with salt and pepper and top with parsley. Drizzle extra-virgin olive oil liberally over the fish portions. Fold the top and bottom edges together and crease several times then crease up the ends of the packets. Arrange the packets on the baking sheet and place in the center of the hot oven.
Bake packets 20 minutes. Serve a packet per dinner plate and cut open at table. Cut lemon into wedges and serve to squeeze down over the hot fish. Pass bread to mop up the cooking juices in the sack.