Pre-heat the oven to 400°F.
In a bowl, combine the fennel, onion, potato, garlic, salt, pepper and just enough olive oil to lightly coat. Cut four 12-inch x 16-inch pieces of parchment paper (you can also buy precut packaged half sheets from any restaurant supply store).
Arrange about a quarter of the fennel mixture in the center of each parchment. Drizzle with 2 tablespoons vermouth or wine per packet, then top with the fish and season the fish with salt and pepper. Top each fish with 1 teaspoon lemon juice, 1 pat butter and some parsley. Fold the papers’ short ends at the middle, folding them over an inch, then a few more turns; fold in the ends to make half-moon shaped packets (sacks).
Roast the fish in the sacks for 20 -25 minutes, then remove from the oven. Serve on plates. Open the parcels carefully and slide the contents away from the paper. Discard the paper.